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Full text of "Inelastic analysis of frame structures including member and joint shears"

INELASTIC ANALYSIS OF FRAME STRUCTURES 
INCLUDING MEMBER AND JOINT SHEARS 



BY 
VINAYAGAMOORTHY BALACHANDRAN 



A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL 

OF THE UNIVERSITY OF FLORIDA IN 

PARTIAL FULFILLMENT OF THE REQUIREMENTS 

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 



UNIVERSITY OF FLORIDA 
1984 






ACKNOWLEDGEMENTS 

The author expresses his gratitude to his adviser and doctoral 
committee chairman, Professor C. 0. Hays, for his guidance and 
enthusiastic encouragement during the conception and development of this 
research, and in the preparation of this report. Thanks are extended to 
Professors M. W. Self and J. M. Lybas of Civil Engineering, Professor 
U. H. Kurzweg of Engineering Sciences, and Professor Z. R. Pop- 
Stojanovic of Mathematics for their participation in the doctoral 
committee. 

The author is greatly indebted to Professor J. H. Schaub, Chairman, 
Civil Engineering Department, for providing a graduate assistantship 
throughout most of this study. Financial assistance provided by his 
fiancee, Ms. S. B. Rasaratnam, during the final period of this research 
is also deeply appreciated. 

Special thanks are due to the Department of Civil Engineering for 
bearing the computer expenses. The computer assistance rendered by the 
consultants of the Center for Instructional 'and Research Computing 
Research Activities is appreciated. The author would like to thank Ms. 
Lynne Parten for the typing of the manuscript. 

Finally, thanks are due to the author's family members and fiancee 
for inspiration, encouragement and forbearance. 






TABLE OF CONTENTS 



PAGE 
ACKNOWLEDGEMENTS i i 

NOMENCLATURE 



VI 

ABSTRACT „ x1 1 

1. INTRODUCTION 1 

1.1 General 1 

1.2 Available Procedures for Nonlinear Inelastic Analysis of 

F rames 2 

1.3 Purpose of this Research 8 

1.4 Outline of Presentation 9 

2. SHEAR CORRECTIONS TO CLASSICAL BEAM THEORY 11 

2.1 General \\ 

2.2 Flexural Deformations 11 

2.3 Shear Deformations 12 

2.4 Approximate Analysis of Beam with Center Load 15 

2.5 Combined Flexural and Shear Deformations 17 

2.6 The Effect of Shearing Force on the Buckling Load 20 

3. DISCRETE ELEMENT SHEAR MODEL 22 

3.0 Introduction 22 

3.1 Geometric Representation of the Discrete Element Shear 

Model 23 

3.2 Deformation Displacement Relations 23 

3.3 Element End Force — Internal Force Relations 25 

3.4 Internal Force-Deformation Relations 26 

3.5 Discrete Element Shear Tangent Stiffness Matrix 27 

3.6 Remarks on Member Loads and Restraints 30 

4. INELASTIC CROSS SECTION RESPONSE FROM NONLINEAR STRESS 
STRAIN CURVE AND TANGENT STIFFNESS METHOD 31 

4.1 General 31 

4.2 Decomposition of Stress Strain Curve Using Masing Model... 32 

4.3 Relationship of Generalized Forces and Deformations 35 

4.4 Incremental Force Deformation Matrix 40 

4.5 Thin Wall Tubular Sections 43 

4.6 Brief Description of the Solution Procedure 44 

4.7 Tangent Stiffness Method 45 

4.8 Modified Tangent Stiffness Method 47 



n l 



PAGE 

5. SHEAR BEHAVIOR AND STRENGTH OF STEEL JOINTS 52 

5.0 Introduction 52 

5.1 Shear Behavior of Joints 53 

5.2 Shear Force-Distortion Relationships for Joints 56 

5.2.1 Krawinkler Model 57 

5.2.2 Fielding Model 60 

5.2.3 Modified Analytical Model 62 

5.3 Four Degree of Freedom Joint Stiffness Matrix 68 

5.4 Member Stiffness Matrix in Four Degree of Freedom 
Structural Coordinates 73 

5.5 General Comments on DRAIN 2D Analysis 77 

6. FRAME ANALYSIS... 79 

6.1 Assumptions 79 

6.2 Outline of Solution Procedure 80 

6.3 Dynamic Analysis. 82 

6.4 Dynami c Equi 1 i bri urn Check 84 

6.5 Damping Constants 86 

6.6 Comparison with Other Methods 87 

6.7 Comment on Static Analysis 88 

7. THE COMPUTER PROGRAM FRAME82 89 

7.0 Introduction 89 

7.1 Main Features and Limitations of FRAME82 90 

7.2 Program Structure 95 

8. VERIFICATIONS WITH ANALYTICAL SOLUTIONS 97 

8.0 Introduction 97 

8.1 Example of Deep Prismatic Cantilever Beam 98 

8.2 Example on Buckling of a Prismatic Cantilevered Beam 102 

8.3 Example on Mass Dependent Damping 105 

8.4 Example on Joint Shear Panel 108 

8.5 Example on Prismatic Frame Buckling Ill 

8.6 Single Story Frame Subjected to 1.5 El Centro Earthquake.. 115 

9. COMPARISONS WITH AVAILABLE EXPERIMENTAL DATA 125 

9.0 Introduction 125 

9.1 Example of Beam-Column Subassemblage 125 

9.2 Example of 3-Story Frame 136 

10. CONCLUSIONS AND RECOMMENDATIONS 164 

10.1 Conclusions 164 

10.2 Recommendations 165 

APPENDIX A - DISCRETE ELEMENT SHEAR MATRICES 168 

A.l Initial Stress Stiffness Matrices 168 

A. 2 Incremental Deformation-Displacement Matrix [B].. 171 

A. 3 Incremental Force-Deformation Matrix [D] 171 

A. 4 Discrete Element Shear Matrices and Other 
Essential Relationships Excluding Geometric 

Nonlinearities 172 

APPENDIX B - CONSTANT AVERAGE ACCELERATION METHOD 174 



TV 



PAGE 
APPENDIX C - INPUT GUIDE FOR FRAME82 176 

APPENDIX D - JOB CONTROL LANGUAGE STATEMENTS 200 

APPENDIX E - GLOSSARY OF FORTRAN VARIABLES IN FRAME82 204 

APPENDIX F - FORTRAN LISTING OF FRAME82 217 

APPENDIX G - SAMPLE INPUT 359 

APPENDIX H - SAMPLE OUTPUT ... 362 

APPENDIX I - DIGITIZED VALUES OF EARTHQUAKE MOTIONS EL CENTRO 

1940 AND EC400-1 410 

REFERENCES .412 

ADDITIONAL REFERENCES 417 

BIOGRAPHY , 418 






NOMENCLATURE 

a undeformed shear panel length parallel to x axis 

A cross-sectional area 

A i Area of i th subrectangle = AWn,- 

A j Area of j th rectangle 

A s effective shear area 

AE axial stiffness 

b width 

b undeformed shear panel length parallel to y axis 

b c column flange width 

[B] incremental deformation-displacement matrix of order 3X6 

c damping coefficient 

C SJ - shear area coefficient for j th rectangle 

[Cj] incremental damping matrix 

d b , d c distances between the centroids of beam and column flanges, 
respectively 

dg girder depth 

[D] incremental internal force-deformation matrix of order 3X3 

E modulus of elasticity 

history dependent stiffness of a component curve 

E for k th component 
E s h strain hardening modulus 

{E}^ dynamic equilibrium error at j th time station 

EI flexural stiffness 



vi 



f x , fy joint forces parallel to x and y axes, respectively 

if} discrete elelment end-force vector of order 6 

{f} joint force vector 

(f(t)} nodal force vector 

{F^(t)} damping force vector 

{F j (t ) } inertia force vector 

{F s (t)} stiffness force vector 

S modulus of rigidity 

Gj modulus of rigidity of the j th rectangle 

G t slope of the joint shear stress-strain curve 

h half length of undeformed discrete element 

h height 

"V h r horizontal distances of the left and right vertical edges of 
the rectangular shear panel from the centroid, respectively 

H projection of the deformed discrete element shear model on the 
undeformed original direction 

I second moment of area 

If moment of inertia of the flange 

^2 second invariant of the deviatoric stress tensor 

k shear area factor 

k a constant 

k s spring stiffness 

[k] tangent stiffness matrix 

[k] c conventional portion of discrete element stiffness matrix 

[k] s initial stress portion of discrete element stiffness matrix 

[k] st , portion of discrete element initial stress stiffness matrix 

[k] sv due to axial and shear forces, respectively 

K(p) complete elliptic integral of the first kind 

[K],[K-|-] tangent stiffness matrix 



1 span 

1 number of linear line segments defining the symmetric part of 
a virgin stress-strain curve 

lj number of component curves that constitute the virgin 
o-z curve for the material of j th rectangle 

m number of input rectangles for a cross-section 

m v , m z couples produced by the shear forces acting along the edges of 
the rectangular shear panel perpendicular to x and y axes, 
respectively 

M moment 

M internal moment contributed by j th rectangle 

[M] mass matrix 

n post -yield stiffness parameter 

"j number of equal division of j th rectangle 

P mean normal stress 

P axial load or applied lateral load 

P cr critical buckling load 

Pj: Euler critical load 

{P} load vector 

Q first moment of area about the neutral axis (Ay) 

R radius of curvature 

S k slope of line segment connecting points k and k-1 of the 

virgin stress-strain or force-deformation curve 

t equivalent thickness of the shear panel 

t c f column flage thickness 

t cw column web thickness 

t s thickness of the shear reinforcement area parallel to the web 

T internal axial force 

Tj internal axial force due to j th rectangle 

[T] transformation matrix 



u x , Uy x and y displacements of the panel, respectively 

u x displacement at point A 

{u} displacement vector 

U strain energy 

v b , v t vertical distances of the bottom and top horizontal edges of 
the rectangular shear panel from the centroid, respectively 

v y displacement at point A 

V shear force normal to the deformed axis 

v j shear force on j th rectangle 

w displacement of member 

w f , w n , deflection due to flexural, normal, shear, and total stresses 

w s , w t respectively 

{w} discrete element end-displacement vector of order 6 

{w} 4 DOF displacement vector for a joint 

l w J 3 DOF displacement vector a member end 

{w} joint displacement vector 

y difference between the displacements of member and member 
chord 

y distance of a point from the neutral axis in a section 

y distance of the centroidal area from the neutral axis 

>i height of i th subrectangle from the centroid of the section 

Y k stress defining the k th component curve 

a damping constant related to mass matrix 

a stiffness degradation factor for a material 

P damping constant related to stiffness matrix 

3 yield stress growth factor for mild steel 

Y a variable of a, s, and At 

Y shear strain 

Y m maximum average shear deformation 



ix 



y shear strain 

Y yield shear strain 

6 a' <S m' l5 s axia1 » flexural, and shear deformations 

A relative joint displacement 

At time increment 

£ flexural strain 

£ c strain at the centroid of a section 

e j strain at the center of i th subrectangle 

eL plastic strain on the plane i alony the direction j 

e l < strain defining the k th abscissae of virgin a-e curve 

e p effective plastic strain 

er^ residual strain of k th component curve 

ert k temporary value of the residual strain of k th component curve 
during iteration 

£ s shear strain 

{e} generalized strain vector for discrete element 

9 angle that line joining the ends of deformed discrete element 
makes with the undeformed element direction 

9 r rigid body rotation 

shear deformation 

8 v' 9 z rotations of y and x axes in a shear panel 

8 A rotation at point A 

v Poisson's ratio 

5 time variable 

n de p second invariant of the plastic strain increment tensor 

o flexural stress 

o history dependent stress of a component curve at a general 
material point 

Q effective stress 



0] stress at the center of i th subrectangle 

a ij stress on the plane i along j direction 

ctJj deviatoric stress on plane i along j direction 

a k k th ordinate of the virgin cr-e curve 

a y uniaxial yield stress 

ar k fictitious stress of the k th component curve at a material 
point 

M generalized stress vector for discrete element 

t shear stress 

t max maximum shear stress 

T „ yield shear stress 

<f> curvature 

*li i>2 angles associated with the discrete element models 

u circular frequency 



Abstract of Dissertation Presented to the Graduate School 

of the University of Florida in Partial Fulfillment of the 

Requirements for the Degree of Doctor of Philosophy 



INELASTIC ANALYSIS OF FRAME STRUCTURES 
INCLUDING MEMBER AND JOINT SHEARS 

By 

Vinayagamoorthy Balachandran 

December 1984 

Chairman: Dr. C. 0. Hays 

Major Department: Civil Engineering 

A computer program, FRAME82, is developed to perform inelastic 

static and dynamic analyses of plane frame structures including member 

and joint shear deformations. The effects of parameters such as 

inelastic material properties and member and joint supports, nonlinear 

geometry, cyclic loading, mass dependent viscous damping, etc., are also 

included in the program. FRAME82 utilizes a newly developed Discrete 

(Finite) Element Shear Model to incorporate the effects of member shear, 

in addition to the Discrete Element Flexural Model that considers only 

flexural and axial deformations. Joint shear panels are assumed to have 

only shear deformations, and flexural and axial deformations are 

ignored. Besides the three regular degrees of freedom, namely, 

horizontal, vertical, and rotational displacement, the program requires 

an additional rotational degree of freedom for each joint to include the 

joint shear deformation effects. 



(i i 



The structure stiffness is formulated from the stress-strain level 
and several inelastic models including Masing are incorporated. The 
program updates the structure stiffness after each iteration within each 
time step and adds any unbalance in "dynamic equilibrium" as a 
corrective load at the beginning of the subsequent iteration. 

The program is verified with several simple structures that have 
either theoretical solutions or analytical results. The agreement is 
very good in most of the examples. The reliability of the discrete 
element shear model and the influence of the parameters that affect the 
structure response are studied. Several structures with experimental 
data are analyzed using FRAME82. The analysis of a three story frame 
tested at the University of California, Berkeley, indicates permanent 
deformations of the joint shear panels, which were not obtained in the 
DRAIN 2D analysis. 

A user input guide with detailed descriptions is presented with 
several examples. 



XI 1 l 



CHAPTER 1 
INTRODUCTION 

1.1 General 
In the design of a structure, it is necessary to satisfy both 
serviceability requirements to avoid functional failure and safety 
requirements to assure safety against structural failure. The 
serviceability requirements impose the need to keep the response of the 
structure in the elastic range and to limit the displacement under 
moderate loading which may occur numerous times during the life of the 
structure. In case of an extreme loading, structural failure must be 
prevented. In order to satisfy the second requirement, the structure 
must have the ability to absorb and ultimately dissipate large amounts 
of energy. It is not economical to design a frame subjected to extreme 
loads occurring during earthquakes of exceptionally high intensity, 
extreme wave conditions or heavy wind storms that have low probabilities 
of occurrence to remain within the elastic or proportional limits. 

The current concept of earthquake-resistant design involves the 
structure remaining elastic or nearly so under the influence of moderate 
earthquakes of frequent occurrences, and the structure yielding locally 
into the inelastic range, but with safety from collapse, even under the 
conditions of the most severe probable earthquake (5, 33). Each 
structural component of a moment resistant frame must be designed such 
that its ductility allows a redistribution of moments without failure of 
the component, until the maximum amount of earthquake energy input is 



applied to the structure, to avoid structural failure under an extreme 
loading. Ultimately, all the energy must be dissipated by internal 
friction and inelastic deformation in both the structural and non- 
structural elements. 

Due to the advent of Finite Element Method techniques and computers 
and the need of the detailed understanding of the behavior of 
earthquake-resistant structures, nonlinear analysis of structures has 
attracted much attention during the past three decades (1-56). 
Nonlinear analysis includes primarily the effects of material and 
geometric nonlinean'ties (22). Material nonlinearity includes nonlinear 
stress-strain curve for frame materials and supports with a nonlinear 
reaction-displacement curve due to nonlinear soil response. The 
nonlinear response is significant in most materials even when the 
loading is monotonic. Load reversals and cyclic loading greatly 
increase the nonlinear effects on frames with inelastic materials. 
Geometric nonlinearity arises from the consideration that points of 
application of the loads of a system are displaced due to large 
deformations, and the analysis can no longer be based on undeformed 
geometry. The axial forces on frame members cause secondary moments. 
The secondary moment can be divided into two components, P-A moment and 
P-y moment. The P-A moment is equal to the axial force P times the 
joint displacement A. The P-y moment is equal to the force P times the 
distance y, where y is the difference between the displacement of the 
member and displacement of the member chord. 

1.2 Available Procedures for Nonlinear Inelastic Analysis of Frames 
Early attempts to model the inelastic response of structures 
subjected to earthquake motion appeared in the form of an elasto-plastic 






approximation to the inelastic behavior of the structure. An elasto- 
plastic model was utilized by Berg (2), Newmark (39), and Penzien (41) 
in the late 1950's to analyze single story frames and by Hanson and Fan 
(19) in the late 1960's to analyze multistory buildings. This model, 
coupled with the numerical integration of the dynamic equations of 
motion, afforded the first detailed insight into the inelastic 
characteristics of buildings during earthquake excitation. 

A bilinear model was utilized by Iwan .(26) to study inelastic 
member behavior in 1961 for simple yielding structures and by Clough, 
Benuska, and Wilson (9), Giberson (16), and Grant (18) in later years. 
Jennings (27) in 1963 utilized a curvilinear approximation for simple 
yielding structures and in 1967 Kaldjian and Fan (29) utilized Ramberg- 
Osgood approximation to the inelastic behavior of structural elements in 
simple structures subjected to earthquake excitation. Goel (17) 
expanded the Ramberg-Osgood model to multistory structures by making use 
of the symmetrical nature of the response of a multistory single bay 
frame. 

Workman (55) developed a program to analyze the dynamic response of 
a multistory single bay braced frame in 1969. The frame is considered 
to have three distinct structural elements. They are Diagonal Cross 
Braces, Girders, and Columns. The diagonal braces are tension carrying 
members with elasto-plastic behavior. Girders are ideal elasto-plastic 
beams and axial deformations are neglected. Columns are elasto-plastic 
beam-columns with axial force effects accounted in the stiffness, 
deflection pattern and plastic moment characteristics of columns. The 
moment -curvature relation is nonlinear in the plastic range due to the 
modification of the plastic moment by the axial force. Nonlinear 



response of the frame is obtained by a numerical procedure. The 
structure is assumed to respond linearly during each time increment. 
However, member properties may be changed from one interval to the 
next. Thus, the nonlinear response is obtained as a sequence of linear 
responses of successively differing systems. 

Latona (36) studied the significance of geometric and material 
nonlinearities in static and dynamic analyses. His analysis included 
partial plastification of a cross-section, spread of plastification 
along the length of a member, inelastic strain reversals and P-A frame 
moments. He divided a cross-section into a finite number of layers. 
Each layer is assumed to have constant stress as of its centroid. He 
utilized an ideal elasto-plastic stress-strain relationship to represent 
the behavior of the material. The member stiffness matrices are 
obtained by integrating over each cross-section to obtain the section 
flexibility coefficients, integrating over the length of the member to 
obtain the member flexibility matrix, and inverting the flexibility 
matrix. Between time increments, geometry of the structure is updated 
by adding the displacements that occurred during the preceeding 
increment to the joint coordinates at the beginning of that increment; 
i.e., P-A moment is included, but P-y moment is not considered. 

Workman and Latona considered only lateral modes of vibration and 
reduced the unknown displacements to one-third the original number by 
assuming negligible inertia loads corresponding to vertical and rotary 
displacements and considering the static equation. They further 
utilized kinematic condensation which simply imposes the condition that 
all joints at a given floor level displace laterally by the same dis- 
placement; i.e., one degree of freedom per story is retained explicitly. 






Hays and Matlock (23) developed FRAME53 to analyze statically 
loaded plane frames using a Discrete Element Model. This analysis takes 
into account the actual stress-strain behavior of the materials of which 
the frame is made. It also handles geometric nonlinearities and 
nonlinear soil support characteristics. Even though, the material and 
support characteristics are specified as nonlinear, they are elastic in 
behavior. The discrete element model is shown in Fig. 1.1 (22). It 
consists of two rigid end bars which are rigidly connected to the 
neighboring elements to preserve vertical, horizontal, and rotational 
compatibility at the nodal points, a middle bar that is rigid in bending 
but extensible, and two rotational springs at the hinges. 

A member is divided into a finite number of elements and thus 
allows member properties, loading, and support conditions to vary along 
its length. The individual members are solved separately to obtain each 
member's stiffness and fixed end force matrices. Since member and 
structure solutions are performed separately, an iterative cycle for 
each member occurs within the iteration of structural joint 
displacements. The P-A and P-y moments are taken care of in the 
analysis by virtue of the large displacement analysis of the element 
model . 

Kanaan and Powell (30) also made the same assumptions as Workman 
(55) and Latona (36) on effective degrees of freedom and kinematic 
condensation. The frame is considered to have the following structural 
elements: (i) Truss bar (ii) Beam Column element (iii) Semi -rigid 
Connection element and (iv) Shear Panel element. All of the elements 
are assumed to have bilinear relationship between force and 
displacement. Yielding is restricted to specific locations. Inelastic 




Figure 1.1 Discrete Element Flexural Model (22' 






axial deformations are neglected in beam-column elements because of the 
difficulty of considering the interaction between axial and flexural 
deformations after yield. Infill panel elements are assumed to have 
shear stiffness only in the XY plane. The shear panel provides 
resistance through shear deformation to relative horizontal and/or 
vertical displacement of nodes it connects. Semi-rigid connection 
elements are used to account for the angle changes that occur between 
connected beams or columns. Damping is included in their analysis. It 
is assumed as a linear combination of mass and stiffness matrices. Only 
P-A moment is incorporated in the program to account for nonlinear 
geometry. 

Santhanam (47) developed FRAME63 which is capable of inelastic 
static and dynamic analysis of plane frames including the effects of 
geometric and material nonlinearities in 1978. This program differs 
from the other available programs due to its capability of handling many 
types of stress-strain relationships. However, the virgin stress-strain 
curve is assumed to be symmetric in tension and compression. Several 
inelastic unloading models, including the Masing Model, were used to 
represent general piecewise linear symmetric inelastic stress-strain and 
force deformation curves are incorporated in their program. 

A member is divided into a finite number of elements which are then 
divided into several layers. The same discrete element model which was 
used by Hays is used to form member stiffness matrix. Three degrees of 
freedom are considered for each node. Both P-A and P-y moments are 
included in the analysis. However, it does not include effects such as 
damping and deformations of panel zones, which are included in the 
program developed by Kanaan and Powell (30). 









8 

The programs developed by Santhanam (47) and Kanaan and Powell (30) 
are the two which handle more parameters which influence the inelastic 
response of a structure. Even though a more general stress-strain curve 
was used by Santhanam, effects of member and joint shears and damping 
are not considered. On the other hand, Kanaan and Powell accounted for 
damping, rigidity of joint and shear deformations due to panel zones, 
but they utilized a bilinear relationship between generalized force and 
generalized displacement. It is to be noted that Kanaan and Powell 
considered neither the inelastic axial deformations of columns nor P-y 
moments. Shear deformation was considered only in shear panels but not 
in beams. 

1.3 Purpose of this Research 
The purpose of this research is to develop a computer aided 
analysis that includes all the parameters such as general stress-strain 
curve for the material, P-A moment, P-y moment, member shear, joint 
shear, viscous damping, etc. The following are the objectives of this 
research, 
(i ) Develop a discrete element model to include the member shear in 

the frame analysis. 
(11) Develop a technique to include connection panel deformation in 

the response analysis of structures subjected to earthquake 

motions. 
(iii) Incorporate the above two features with viscous damping into 

FRAME63 without disrupting the existing capabilities of the 

program to develop a new program, FRAME82. 
(iv) Study the influence of each parameter on the behavior of the 

structure. 






(v) Compare the predicted response with the available experimental 
data and analytical results. 

1.4 Outline of Presentation 

Chapter 2 reviews the elementary beam theory and focuses on the 
influence of shear on deflection and buckling load. A new discrete 
element model is developed in Chapter 3 to include the member shear. 
Chapter 4 is devoted to the derivation of cross-section behavior from 
the material nonlinear stress-strain curve. It is very similar to that 
discussed by Santhanam (47) but the incremental force deformation matrix 
is derived for the discrete element shear model. A technique to 
incorporate the joint deformation is discussed in Chapter 5. However, 
this method is restricted in its present application to the rectangular 
frames with no diagonal bracings. A numerical scheme is presented in 
Chapter 6 to solve the governing coupled frame equations. Even though 
mass and stiffness dependent damping are included in the presentation, 
only mass dependent damping is embodied in the program. The main 
aspects of the program FRAME82 are discussed in Chapter 7. In Chapter 
8, analytical solutions of simple structures are compared with the 
results obtained from FRAME82. Comparison between the available 
experimental data and predicted behavior of these structures by FRAME82 
is included in Chapter 9. Chapter 10 summarizes the scope of the 
present research and includes recommendations for further research. 

Appendix A contains the required matrices to obtain tangent 
stiffness matrix for a discrete element. The constant average 
acceleration method is presented in Appendix B. An input guide with 
detailed explanations is given in Appendix C. Appendix D deals with the 
job control language statements and space requirements of the storage 



10 



devices. Appendices E, F, G, H, and I include a glossary of FORTRAN 
variables, FORTRAN listing of FRAME82, sample input, sample output, and 
digitized values of earthquake motions used in example problems. 






CHAPTER 2 
SHEAR CORRECTIONS TO CLASSICAL BEAM THEORY 

2.1 General 



The classical beam theory produces errors in both predicted 
stresses and strains. The error in stress can generally be ignored in 
the static loading of structure made of ductile materials, but 
consideration should be given if brittle materials or fatigue conditions 
are involved. The error in strain chiefly affects the deflections, 
underestimating deflections, while overestimating buckling loads and 
natural frequencies. These errors are generally negligible in slender 
beams under usual types of loading but are serious in short beams and 
beams under closely spaced loads which alternate in direction. This 
error in strain is also likely to be important in "sandwich" beams, 
latticed beams and flanged beams, where most of the material is 
concentrated in outer faces and inner part is lightened until it is just 
strong enough to resist transverse shear force. The resulting shear 
strain produces additional deflection which is of the same order of 
magnitude as of the flexural deflection that is given by the classical 
theory. This chapter deals with the improvements that could be made to 
the classical beam theory to obtain better estimates of deflection (14, 
52). 

2.2 Flexural Deformations 
The classical beam theory, which incorporates several simplifying 
assumptions, predicts deflection only due to flexural deformations. The 

11 



12 

fundamental assumptions are straight beam, homogeneous, isotropic and 
elastic material, plane sections remain plane during bending 
deformations, small deflections compared to the original length of the 
beam, and beam loaded in a plane containing one of the principal moment 
of inertia axes (49). The radius of curvature R of the axis of the 
beam, flexural stress a at a distance y from the neutral surface, 
bending moment M, second moment of area I, and modulus of elasticity E 
are related by the following expression (25, 54): 

o/y = E/R = M/I (2>1) 

The curvature of the neutral axis given by 

1/R = ±d 2 w/dx 2 /[l+(dw/dx) 2 ] 3 / 2 (2.2) 

is approximated by 

1/R = ±d 2 w/dx 2 (2>3 n 

where w is the deflection. Substituting Eq. 2.3 in Eq. 2.1 gives 

d 2 w/dx 2 = +M/EI , z 4) 

This expression is a force deformation relation for a beam 
subjected to pure bending. However, it represents a good approximation 
of the beam behavior when the deformations due to shear and axial loads 
are insignificant. The sign in Equation 2.4 has to be chosen such that 
it will be consistent with the choice of coordinate axes and the 
definition of positive direction for bending moment. Adoption of the 
sign conventions illustrated in Fig. 2.1 leads to 

d 2 w/dx 2 = M/EI / 2 5 x 

2.3 Shear Deformations 

Since the present study deals with member shear effects 

extensively, a detailed derivation of force deformation relation for 

shear is presented in this section. The shear stress x in a beam at any 



13 



w 




Figure 2.1 Coordinate System and Sign Convention for Bending Moment and 
Shear 






(a) Pure Shear Deformation (b) Cross Section 

Figure 2.2 Deformation of a Beam Element due to Shear 









14 

transverse cross section in its length, and at a point a perpendicular 
distance y from the neutral axis, resulting from bending is given by 

t = VAy/Ib or VQ/Ib ( 2 .6) 

where V is the applied shear force; A is the area outside of the section 
parallel to the neutral axis at a distance y (shaded region in Fig. 
2.2); y is the distance of the centroid of area A from the neutral axis; 
I is the second moment of area of the complete cross section; b is the 
breadth of the section at position y; and Q is equal to A times y (25). 

A beam of finite length AX shown in Fig. 2.2 with its cross section 
is subjected to a shear force V. Castigliano's first theorem will be 
used to obtain the shear deflection under pure shear loading. The 
strain energy U of the beam element is 

U = //(t 2 /2G)dydzAX (2<7) 

= (AX/G)//((VQ) 2 /2I 2 b 2 )dydz (2 . 8 ) 

Hence, the shear deflection 6 is 

5 s = -3U/9V = -(AX/G)//(Q 2 /I 2 b 2 )Vdydz 

= -(AXV/I 2 G)//(Q 2 /b 2 )dydz = Y AX (2.9) 

i.e. y = -(V/I 2 G)//(Q 2 /b 2 )dydz = -kV/A G (2,10) 

where k = (A s /I 2 )//(Q 2 /b 2 )dydz ( 2# il) 

in which /\ s = effective shear area, k = shear area factor, and y = 
change in the slope of middle surface due to shear deformations. A is 
equal to the total area for rectangular and circular sections and the 
web area for I-sections. The value of k, which is depended on the shape 
of the cross section, is 1.2 for rectangle, 1.11 for circle and nearly 
1.0 for most of the I-sections (52, 53). 






15 

2.4 Approximate Analysis of Beam with Center Load 
The material presented in this section is selected from the book by 
Donnell (14). The relative magnitudes of the deflections due to 
flexural, shear, and normal stresses are studied considering a simply 
supported beam of rectangular cross section with center load P, shown in 
Fig. 2.3. 

The flexural deflection w f due to longitudinal bending stress is 
predicted by classical beam theory as 

w f = -P£ 3 /48EI = -P£ 3 /4Eh 3 (2.12) 

The shear deflection w s caused by transverse shear strain is 
approximately calculated by assuming uniform shear stress distribution 
over the cross section (instead of the parabolic distribution with zero 
stress at the top and bottom fibers). This assumption requires the 
cross sections to remain plane and vertical. The shear strain e = 
P/2hG is the angle between the cross sections and the top and bottom 
surfaces, where P/2 is the total shear force. Therefore, 

w s = -e^/2 = -P£/4hG = -(l+v)P£/2hE (2.13) 

Normal strains which dre developed by both transverse and 
longitudinal stresses produce negligible changes in the transverse 
length. However, an appreciable effect is produced by the longitudinal 
expansion, of the material directly under the load P due to Poisson's 
ratio effect. There is a similar expanion under the end reactions P/2 
but it has a negligible effect on deflection. Assume that P is 
uniformly distributed over a small width A and the lateral compressive 
stress varies from P/A at the top to zero at the bottom. Due to 
Poisson's ratio effect the top will expand horizontally a 
distance (P/A) (v/E) (A/2) = vP/2E on each side of the center line and 



^ 



16 



r£r 



WF 



(a) Elevation and Cross Secti 



on 




^T 




w. 



Pi j 



(b) Flexural Deflection 



w. 



w 



P/2 



(c) Shear Deflection 



P/2 



w 



w 



P£ 3 2(l+v)h 2 
" 48EI 72 




r w = 



3 ? 

PJT vh* 

wr^2" 



(d) Deflection w due to Normal Stresses 



Figure 2.3 Rough Analysis of a Beam with Center Load 



17 

the expansion linearly decreases to zero at the bottom. Therefore, the 
vertical side at the center will rotate through an angle of (vP/2E)/h = 
vP/2hE. Hence, the deflection w n due to normal stresses is 

w n = (vP/2hE)l/2 = vp£/4hE (2.14) 

Assume that the total deflection can be obtained by adding the 
deflections that are derived considering each deformation independently. 
The deflections w f , w s , w n and the total deflection w t can be written in 
the form 

w f = -P£ 3 /4Eh 3 

w s = -(P£ 3 /4Eh 3 )[2(l+v)h 2 /£ 2 ] 
w n = (Pi> 3 /4Eh 3 ) (vh 2 /J£ 2 ) 

w t = w f + w s + w n = -(P£ 3 /4Eh 3 )[l+(2+v)h 2 /£ 2 ] (2.15) 

The second term in the bracket of w t represents the correction to 
the classical elementary formula. It is to be noted that deflection due 
to transverse normal stress is proportional to and much smaller than 
that due to transverse shear strain. The former can therefore be taken 
into account by multiplying the deflection due to transverse shear by a 
numerical factor of the order of unity. 

2.5 Combined Flexural and Shear Deformations 
Timoshenko assumed that the deflection due to bending and shear can 
be determined by superposition (54). This could be justified by closely 
examining the effect of shear deformations on a beam. For a beam of 
rectangular cross section, Eq. 2.6 indicates a parabolic shear 
distribution as shown in Fig. 2.4 (a). Therefore, the shear 
strain y = x/G must vary in a similar fashion. This implies originally 
plane cross sections distort in the manner shown in Fig. 2.4 (b). 
Figure 2.4 (c) displays the deformed plane sections of a rectangular 






18 



w 




w 




(a) Shear Stress Distribution on 
a Rectangular Cross Section 



(b) Elevation of the Warped Beam 
of Finite Length AX 




(c) Rectangular Cantilevered 

Beam with Warped Cross Sections^ 

Figure 2.4 Effect of Shear on Plane Cross Sections 




-///// 

y 

(a) 



V + dV 





Figure 2.5 Cantilevered Col 



umn 












19 

canti levered beam due to flexural and shear deformations. The shearing 

strains are zero at the upper and lower surfaces and equal to x /G at 

the neutral surface. Hence, the deformed sections remain normal to the 

longitudinal fibers at the upper and lower surfaces and inclined to the 

neutral surface at an angle equal to the shear strain t . /G. The 

max 

warping of all cross sections is the same as long as the shear force 

remains constant. Hence, shear stresses x do not contribute to the 

longitudinal strains and the distribution of the longitudinal 

stresses a is the same as in the case of pure bending. A more elaborate 

theoretical investigation reveals that the influence of shear 

deformations on flexural strains and stresses is very small, even when 

the shear force varies along the length of the beam (54). Hence, it is 

reasonable to add the deflections obtained in separate flexural and 

shear analyses to obtain the total deflection. Moreover, the effect of 

transverse normal stresses in the total deflection could be included in 

the analysis by properly modifying the shear area factor. 

Using the principle of superposition, 

w t = w f + w s (2>16) 

Differentiating twice with respect to x gives 

d 2 w t /dx 2 = d 2 w f /dx 2 + d2 V dx2 (2.17) 

From Equations 2.5 and 2.9 

d 2 w f /dx 2 - M/EI 

dw s /dx = y 
Substituting the above relationships in Eq. 2.17 yields 

d 2 w t /dx 2 = M/EI + dy/dx 
i.e. d 2 w t /dx 2 - dY/dx = M/EI (2.18) 



20 

Equation 2.18 is the general force deformation relationship that 
includes the effects of flexural and shear deformations for a beam. 
2.6 The Effect of Shearing Force on the Buckling Load 
Consider the column shown in Fig. 2.5 to derive an expression for 
buckling load including the shear effects. The shear force V and the 
moment M at any section can be obtained considering the equilibrium of 
the column above that section. Hence, 
V = -Pdy/dx 
M = P(A-y) 
Substituting the above expressions into Eq. 2.18 gives 
d 2 y/dx 2 - (d/dx)(-k/A s G)(-Pdy/dx) « P(A-y)/EI 
For a prisimatic column of constant cross section the above equation 
becomes 

(d 2 y/dx 2 )(l-kP/A s G) = P(A-y)/EI 
i.e. d 2 y/dx 2 = [P/EI(l-kP/A s G)] (A-y) (2.19) 

Solving the above differential equation for critical load would give 

P/EI(l-kP/A s G) - u 2 /4L 2 
from which 

P cr = P E /(l+kP £ /A s G) (2>20) 

where, P E = tt 2 EI/4L 2 , 2 21) 

represents the Euler critical load for this case and L is the original 
length of the column. Thus, owing to the action of shearing forces, the 
critical load is diminished in the ratio 

1/(1 + kP E /A s G) 
In the case of solid columns this ratio differs but very little from 
unity. But in the case of built-up columns consisting of struts 
connected by lacing bars or batten plates, the ratio may vary a lot from 



21 



unity and the effect of shear deformations may become of practical 
importance. For more informational refer to Theory of Elastic Stability 
by Timoshenko and Gere (53). 






CHAPTER 3 
DISCRETE ELEMENT SHEAR MODEL 



3.0 Introduction 
Discrete and Finite Element Methods are similar. Both methods 
require the structure to be divided into a finite number of elements, 
the behavior of which is specified by a finite number of parameters. 
The solution of the structure as an assembly of its elements follows 
precisely the same rules applicable to standard discrete problems 
(56). The basic difference between these two methods is that a 
continuous displacement function is used for each element in the Finite 
Element Method, and displacements are "lumped" at a finite number of 
points within an element in the Discrete Element Method. The points at 
which the displacements are lumped are referred to as hinges in this 
presentation. Division of members into a finite number of elements 
facilitates the handling of the geometric nonlinearity, i.e., P-a and 
P-y moments, and any variation in the member section properties, in the 
analysis. The hinges are convenient points for lumping the element 
deformations. Then nonlinear material force-deformation response can be 
monitored at these hinges. Discrete Element Flexural Model developed by 
Hays and Matlock (22) includes flexural and axial deformations, but 
shear deformations are ignored. The discrete element shear model that 
is developed in this chapter incorporates the effects of axial, 
flexural, and shear deformations of the members in the analysis. 



22 



23 

hi Geometric Representation of the Discrete Element Shear Model 

Figure 3.1 (a) displays the geometric representation of the 
discrete element shear model with the element end displacements and 
deformations. It consists of two rigid bars, which are rigidly 
connected to the adjacent elements to preserve horizontal, vertical, and 
rotational compatibility at the nodes. Each bar is of length h and the 
undeformed length of the element is 2h. Axial, flexural, and shear 
deformations are lumped at the center of the element and the 
corresponding internal forces are defined at the center of the deformed 
element as shown in Fig. 3.1 (b). Axial deformations 6 , flexural 
deformations & m (change in angle between the two rigid bars), and shear 
deformations 6 g correspond to axial force T, bending moment M and shear 
force V at the center of the element. 

3.2 Deformation Displacement Relations 
The element end displacements wj' through w 6 completely define the 
element deformations 5 a , « m , and 6 g . The deformations can be obtained 
in terms of the end displacements by a simple geometric analysis of 
model shown in Fig. 3.1 (a). 

The angle which the line joining the ends of the deformed element 
makes with the undeformed element direction is given by 



1 w 5" w 2 
tan ^h+w 4 - Wl ) (3.1) 



Projection of the deformed element on the line connecting the ends of 
the deformed element gives 

V ( 2h ^ 4 -w 1 ) sece - h cos(w 3 -6) - h cos(w 6 -e) (3.2) 



24 




(a) Undeformed and Deformed Positions 




(b) Forces 



Figure 3.1 Discrete Element Shear Model 






25 

Projection of the deformed element on the normal to the line connecting 
the ends of the deformed element gives 

6 S = h sin(w 3 -e) + h sin (w g -8) (3.3) 

The discrete angle change 5 is 

6 m = w 6 " w 3 (3.4) 

Equations 3.1 through 3.4 are the deformation displacement relations. 
They are valid for large displacements since no small displacement 
theory approximations are made. 

Define the generalized strains {e} as 

{£}t = [ V W (3.5) 

and the element end displacements {w} as 

M* = Cw 1$ w 2 , w 3 , w 4 , w 5 , w 6 ] (3 . 6) 

Then the incremental relationships take the form 

{de} = [B]{dwj (3<7) 

where [B] is a 3X6 incremental deformation displacement transformation 
matrix such that 



8s. 



U 3w, (3.8; 



3.3 Element End Force — Internal Force Relation: 



Consider the equilibrium of the free bodies of the rigid bars in 
Fig. 3.1 (b) to obtain the relationship between the element end forces 
and the internal forces. Resolving the forces in the horizontal and 
vertical directions, and taking moment about the end, for each bar give 
the following relations: 

f 1 = -T cos 6 - V sin 8 ,g g ^ 

fg = "T Sin 8 + V COS 9 /g jq\ 



26 



6 



6 



f 3 = -M + V[h cos (w 3 -8) + -|] + T[h sin (w 3 -9) - -|] ( 3 .il) 

f 4 = T cos 6 + V sin 9 (3.12) 

f 5 = T sin 9 - V cos 8 (3a3) 

f 6 = M + V[h cos (w 6 -6) + -|] + T[h sin (w g -9) - I|] (3. 14) 

Equations 3.9 through 3.14 are the end force internal force relations. 
Define the generalized stress vector {a} as 

M* = ET, M, V] (3>15) 

and the element end force vector {f} as 

i f l = [f p f 2 , f 3 , f 4 , f gf f g ] ( 3#16) 

It is proved in Section 3.5 using virtual work that 

If} - nrfw (3>17) 

The set of transformations given by Equations 3.7 and 3.17 is called 
contragradient (56). However, the end force vector and internal force 
vector of the discrete element shear model do not satisfy Equation 
3.17. The inequality is a function of second order deformation terms 
and occurs because the shear model is not a pure geometric model. The 
accuracy of the discrete element shear model is illustrated by the 
examples of Chapters 8 and 9. 

3.4 Internal Force-Deformation Relations 
For linear elastic materials, the following internal force- 
deformation equations hold true: 

T - AE a 

2ha (3.18) 

M - '-I £ 

2h" m (3.19) 

, A G 
V = 1 s x 

k 2h s (3.20) 

where AE, EI, and A S G are area times modulus of elasticity, area times 
second moment of area, and effective shear area times modulus of 






27 

rigidity respectively, and k is shear area factor. The curvature at the 
hinge is approximated by dividing the discrete angle change by 2h. The 
axial and shear strains are respectively taken as 6 & /2h and 6 /2h. For 
the Equations 3.18 through 3.20 to be correct, the curvature, axial 
strain, and shear strain need to be small but the displacements need not 
be small . 

For nonlinear stress-strain curves, the relationships between 
internal forces and deformations can be obtained using the numerical 
integrations procedure as explained in Chapter 4. Symbolically, 
Equations 3.21 through 3.23 represent these relations. 

T = T(5 a' 5 m' 6 s ) (3.21) 

M = M(5 aJ 5,6) ,„„ 

x a ' m' s y (3.22) 

V = V(5 5,6) »,,m 

a' m' s' (3.23) 

Assume that incremental generalized stresses are related to the 

incremental generalized strains by the following expression: 

{da} = [D]{de} (3<24) 

where [D] is a 3X3 incremental force deformation matrix and D,, is given 
by 

3a. 

D . — 1 

ij 3s, (3.25) 

3.5 Discrete Element Shear Tangent Stiffness Matrix 
The tangent stiffness matrix [k] of order 6X6 for the discrete 
element shear model is defined as 

{df} = [k]{dwj (3>26) 

where {f} and {w} are the member end force and displacement vectors of 

order 6 and 

3f, 
k. . 



ij 3w. (3.27) 

J 






28 

Forces {a} and {f} keep the discrete element model under equilibrium. 
Therefore, principle of virtual work, the virtual work done by the 
forces on a equilibrium system due to virtual displacement is zero, 
leads to 

^ ■ »*** (3.28) 

From Eq. 3.7 

■ {««} ■ CB]{6w} (3<29) 

In view of the above expression, Eq. 3.28 becomes 

*& ■ ***** (3.30) 

Hence, 

~ f = *** (3.31) 

Differentiation of the above equation results in 

df = B t da + dB t 
In tensor notation, Eq. 3.32 can be written as 



2 (3.32) 



df i = B ki da k + dB ki CT k (3.33) 

Substitution of Eq. 3.24 and chain rule expansion for dB ki into the 
above equation gives 

df i = B ki D U de Z + B ki,j dw j a k (3.34) 

Substituting Eq. 3.7 and 3.8 into Eq. 3.34 yields 

df i = CB ki D k£ B £j + a k e k,ij^ dw j (3.35) 

Thus, tangent stiffness matrix k^ is given by the following tensor 
equation: 

k ij = B ki D ki B £j + a k e k,ij (3.36) 

In the explicit form, the above equation can be written as 



3 3e 3 3a 3e 3 3 2 , 

k . S i 1 V i * x y _ k 

1J k«l 3w £-1 3s 3w. k=l CT k 3w.3w. 
1 * J 1 J 



(3.37) 






29 



This equation takes the following matrix form: 

Ck] = [k] c + Ms (3.38) 

where 

M c - [B] 1 [D][B] (3>39) 

Matrix [k] s is called the initial stress stiffness matrix and is 

due to second term of Eq. 3.37, that contributes to k^-. A pure rigid 

body motion of the discrete element produces no internal stresses a, and 

K 

Ck] s will be a null matrix. Initial stress matrix is computed by adding 
the terms, obtained by multiplying initial stress with the corresponding 
second partial derivatives of the deformation displacement equations. 
It can be observed from Eq. 3.4 that 

2 

3w~3w~ = ° for 1 » J - 1>6 (3.40) 

which implies that there is no contribution to the initial stress matrix 
from the initial bending moments. Hence, [k] s can be divided for 
computational convenience into two components, [k] st and [k] sv , which 
are due to axial and shear forces respectively; i.e. 

[k] s = Ck] st + [k] sv (3#41J 

The conventional portion of the stiffness matrix [k] c is due to the 
first term of Eq. 3.37. This can easily be computed using the 
conventional triple matrix product given in Eq. 3.39. The matrices [B], 
CD], Ck] st , and [k] sv are provided in Appendix A. It also contains the 
above matrices for small displacement analysis together with deformation 
displacement relations and element end force internal force relations. 



30 

3.6 Remarks on Member Loads and Restraints 
Member loads and restraints are not considered in the above 
development of force displacement equations for a single discrete 
element shear model. Member loads are discretized into concentrated 
loads acting at the member stations and included in the member solution 
as nodal loads. The same procedure is applicable even to member 
restraints, for which a series of equivalent concentrated springs are 
used at the member stations. More information is available in 
References 22, 23, and 47. 



CHAPTER 4 

INELASTIC CROSS SECTION RESPONSE FROM NONLINEAR 
STRESS-STRAIN CURVE AND TANGENT STIFFNESS METHOD 



4.1 General 



e 



This chapter outlines the method utilized in FRAME82 to obtain th 
inelastic force deformation response of a cross section. It is an 
extension of the method that was adopted by Santhanam (47) in his 
program FRAME63. In addition to the axial and flexural deformations 
considered by Santhanam, shear deformations are also included in this 
derivation. It is to be reminded that FRAME82 preserves all the 
features in FRAME63 and FRAME53, which include inelastic, and nonlinear 
and linear elastic flexural analyses (22, 47). Only the inelastic cross 
section response related to the discrete element shear model is 
presented herein. Tangent stiffness method, which is used to solve a 
general nonlinear system of equations is also reviewed. 
Assumptions and Limitations 

A cross section can be constructed of one or several materials of 
different stress-strain behavior. It is assumed that a cross section 
can be represented by a series of rectangles. Of course, this is an 
approximation for a section composed of nonrectangular pieces. It is 
also assumed that virgin stress-strain curve is defined by a set of 
piecewise linear segments. Inelastic analysis is restricted to the 
virgin stress-strain curves which exhibit symmetrical behavior in both 
tension and compression. The method discussed herein is developed for a 



31 



32 

section entirely composed of rectangular pieces whose virgin stress- 
strain curves are piecewise linear and symmetrical in tension and 
compression. 

The internal forces, namely axial force, bending moment, and shear 
force are listed as functions of axial, flexural, and shear deformations 
in Equations 3.21 through 3.23 of Chapter 3. In spite of the above 
general assumption, to be more realistic, axial force and bending moment 
are assumed as functions of axial and flexural deformations and shear 
force is assumed as a function of shear deformations alone. This 
assumption leads to the following mathematical representation for 
internal forces: 

v a' m' (4.1) 

M = M (V 6 m) (4.2) 

V = V <V (4.3) 

which implies that interaction between the flexural and shear stresses 

is ignored. This is justified by the principle of superposition 

explained in Section 2.5. 

Next, a linear strain variation is assumed over the depth of the 
section to obtain the relations for axial force and bending moment in 
terms of axial and flexural deformations. Shear strain in a member is 
generally small compared to the yield shear strain of the material. 
Hence, a linear elastic shear stress-strain behavior is assumed in 
FRAME82 for member materials. However, this could be extended to 
include very general shear stress-strain curve. 

4.2 Decompositi on of Stress-Strain Curve Using Masing Method 
The . procedure explained in this chapter is applicable to any 
generalized relations such as moment-curvature, force-sway, etc., that 



33 

exhibit similar behavior as of the stress-strain curve. Consider the 
virgin stress-strain curve described by the linear segments 0-1-k-A in 
Fig. 4.1 (a), defined by the coordinates (e k ,a k ), k=l,£. The curve can 
be represented by l idealized elastic-plastic units or "components." 
The inelastic response of the given curve can be obtained by adding the 
responses of each idealized elastic-plastic components. The k th 
component displayed in Fig. 4.1 (b), defined by (e k , Y k ) is derived from 
Equations 4.4 through 4.6: 

Y k = E k £ k for k=l,i (4.4) 

where E R = S k -S k+1 for 1<k<£ (4>5) 

and E k = S k for k-* (4.6) 

S k is the slope of the linear segment 1-k given in Fig. 4.1 (a). 

Consider the particular stress-strain path shown in Fig. 4.1 (a), 
stressed to position A from the origin and then unloaded to position B. 
The stress a and slope E at any point on the path are obtained as 



° \h a (4.7) 



E = F F 

L k=l t (4.8; 



where a and E are the history dependent stress and slope of the k th 

component corresponding to strain e. Note that E = E. when the 

material is in the "elastic" region and zero otherwise. 

Behavior of an Ideal Elastic-P lastic Component Curve and Su mmation 
Procedure 

The idealistic behavior of the k th elastic-plastic component is 
shown in Fig. 4.1 (c). A represents the equilibrium position at the end 
of (n-1) th load increment and er k represents the corresponding residual 






34 




(c) 

klh ideal elastic 
plastic component 
unit 



Figure 4.1 Decomposition of General Nonlinear Symmetric Stress-Strain 
Curve (47) 












35 

strain, used to keep track of the deformation path of the k th 
component. C represents an intermediate point during interaction when 
equilibrium is not yet established. ert k is a temporary variable to 
denote the residual strain corresponding to point C. If the loading 
decrement at the n th load step is considerably small, C will be on the 
"elastic" line through A and ert k will coincide with er k . Point C will 
be on the "plastic" line through A if the new load step is an 
increment. A fictitious stress ar k shown in Fig. 4.1 (c) is used later 
in the Equation 4.9. The flow chart in Fig. 4.2 illustrates the above 
explained procedure to obtain history dependent stress a and slope Q for 
a given strain increment. Note that the check for elastic or plastic 
response of the component is made with respect to er k rather than the 
temporary variable ert k . 

4.3 Relationship of Generalized Forces and Deformations 
A general cross section is shown in Fig. 4.2 (a) with positive 
coordinate directions. The assumed linear strain distribution over the 
depth of the section is given in Fig. 4.3 (b). The bending moment at 
the section is defined about the Z axis through the geometric 
centroid. Tensile strain and the curvature that causes more tensile 
strain at the bottom fiber than at the top, are considered positive in 
this presentation. 

A cross section is defined as a series of m rectangles (j = 1, m), 
each rectangle being of single material of known virgin stress-strain 
curve as shown in Fig. 4.1 (a). Let stress-strain curve of the j th 
rectangle have l. components (k = 1, l ■ ) . Then each j th rectangle is 
divided into rij subrectangles of equal depth (i = 1, n,-). It is 
recommended to use ten equal divisions for a rectangular cross section 






36 



NO , 



YES 



"Elastic" 



E = E, 



o = (e - cr . )*E 

ert = er. 
k k 



o = 
Q = 



First iteration of 
a new load step 



YES 



DO k = l.g. 



".k = Crt k 



Enter with z 



DO k = 1,2, 



"k" * \ 



"Yielding" 
NO 



E = 



c > cr 



iL 



YES 



o = Y, 



Grt k = E " e k 




a = o+a 
Q = Q+E 



RETURN 



Figure 4.2 Flow Chart for Decomposition of General Nonlinear Symmetric 
Stress-Strain Curve (47) 






Y 



37 



th 
J 
ectangle 


. 




gg 


-- A. 

l 


Y. 

l 

7 i 






-- 










— 






— 




u 



(a) A general hybrid section 



(b) Strain (c) Stress 
Distributions Distributions 



Figure 4.3 Cross Section Definition (47) 






38 

and two to four divisions of the flange and four to six divisions on the 
web for an I-section to obtain good results. 

The stress at each subrectangle is assumed uniform over the entire 
depth of the subrectangle and the strain at the center of the 
subrectangle is used to obtain this stress. Figure 4.3 (c) shows the 
typical assumed stress distribution of a cross section. 

Referring to the Figures 4.1 (a) and 4.3, and using Equation 4.7, 
the longitudinal stress ^ on the i th subrectangle is 

l . 
J 

*1 " k il (°r k + E k e k ) (4#9) 

in which 



E k E k (4.10) 

for elastic case 



CTr k = " E k £r k (4.11) 



and 



E k = ° (4.12) 

for plastic case 
aP k = ±Y k (4.13) 

and z s is the longitudinal strain at the center of i th subrectangle. 

The longitudinal strain e 1 can be written in terms of the strain e 
at the center of the section and curvature <fs as 

e i = £ c " ^i (4.14) 

Substitution of Eq. 4.14 in Eq. 4.9 gives 

Z . 
J 

CT i =k E =l K + E "k e c " E "k^i) (4.15) 



39 



The axial force T- in the j the rectangle is 



T j % = \ °1 A i (4.16) 

A. n j 

= ^i E =1 a i (4.17) 

Hence, the axial force T at the section is given by 

m 
T = j = i T J (4.18) 



m A . n j 



- Aj "J »j 



7-1*7 1=1 k-1 ^^ ***'' E k* y i' K-20) 

The contribution Mj by the j th rectangle to the total bending 

moment M is 



M j = : E =1 a i Vi (4.2i) 

A. n j 
= -^J i E =1 °i y i (4.22) 



Hence, the total moment is given by 



m 

3=1 

m A. n j 



M = E M j (4.23) 



"A *7 i=i ™ ^ 



40 



■ A "j *J 



j-l n j i=l * k-1 r k c k 1 ( ] 

The shear force V on the j th rectangle is 

V j = C sj A j G J Y (4.26) 

where 

Y = shear strain 

Gj = modulus of rigidity of the j th rectagle 
C SJ - = shear area coefficient, equal to inverse of the shear 
area factor k of the j th rectangle. 

Recommended values of C sj for a typical I-section are, for flanges and 

1.0 for web. 

Thus, the total shear V at the section is 
m 

V =.*! V j 0-27) 

m 
-T^C^AjBj (4.28) 

The axial force, bending moment, and shear force at the cross 
section are given respectively by Equations 4.20, 4.25, and 4.28. 
4.4 Incremental Force Deformation Matrix 

The incremental internal force deformation matrix is defined by Eq. 
3.24 and given in Eq. 3.25. 

9a. 
1-e. D. =^1 for f-1-3 and j = l-3 (4.29) 

j 

The generalized stress {a} and strain {e} vectors are defined in 
Equations 3.15 and 3.5. 



i.e. [a} 1 = [T, M, V] 



(4.30; 






and 



<«'* = [ V V V 



Therefore, 3X3 matrix [D] can be written in the matrix form as 



41 



(4.31) 



[D] = 



3T 9T 3T 



36 36 m 36 
a m s 



3M 3M 3M 



36 36 m 36 
a m 



3V 3V 3V 



L 



36, 36 96 



(4.32) 



The relations given in Equations 4.1 through 4.3 for T, M, and V yield 



3T m 3M ,. 3V . 3V 

36 ~ 36 36 " 36" 
S S a m 



= 



(4.33) 



Hence, [D] can be written as 



[D] 



3T 3T 



36 36 



m 



3M 3M 



36 36 



3V_ 
36 



(4.34) 



Assuming the strains are small, displacements need not necessarily 
be small, axial strain, curvature, and shear strain can be expressed as 
in Equations 4.35 through 4.37: 



e c " V 2h 

6 = a 72h 

m 

Y = 6 s /2h 



(4.35) 
(4.36) 
(4.37) 



42 



Substitution of the above equations in Eq. 4.34 leads to 



[D] 



1 
7h 



3T 
3e 



3M 
3e 



3T 
3<f) 



3M 

3<j> 



£f o 



L 



(4.38) 



51 



av 

3Y 



All the derivatives in Equation 4.38 can be easily obtained from 
Equations 4.20, 4.25, and 4.28. Remember that ar k assumes a discrete 
constant value for a particular load increment and does not vary 



with e and d>. 
c r 

Therefore, 



3ar k 3ar k 



3£ 



3<j> 



(4.39) 



Differentiation of Eq. 4.20 with respect to z yields 



3e c J-l n j 1=1 k-1 k 

m A . n j 
= E -i Z E. 

J-l "j 1-1 1 



(4.40; 



(4.41, 



Note that Eq. 4.8 is substituted in Eq. 4.40 to get Eq. 4.41. 
Similarly, differentiation of Eq. 4.20 with respect to * yields 



3M 
3<j> 






m A_. n j , *j 



2 
— E y. Z E, 

j-l j i=l k=l 



[4.42) 



43 

3M J A j °J 2 

9 * V-l n J. 1-1 *' Ei (4 ' 43) 

Differentiation of Eq. 4.20 with respect to t Q and of Eq. 4.25 with 
respect to <f> give the same results. Thus, 

u m_ m A j n J *J 

3 * " 9£ c ~ V=i ^7 i=i yi k-i Ek (4 * 44) 

m A, n j 
- f ml nJ & >1 Ei (4.45) 

Finally, differentiation of Eq. 4.28 with respect to y yields 

9V_ m 

9 ^ = j!i C sj A J G j (4.46) 

Incremental internal force deformation matrix [D], also known as 
the instantaneous tangent stiffness matrix of the element, can be 
computed using the Equations 4.38, 4.41, 4.43, and 4.45. Matrices [D] 
of general, and linear elastic and constant prismatic elements are 
listed in Appendix A. 

4.5 Thin Wall Tubular Sections 
The program allows input of a member with thin wall tubular cross 
section. The cross section is subdivided into 20 equal radial segments. 
A pair of radial segments on either side of the y-axis is combined to 
obtain the properties of the equivalent rectangle. Thus, ten equivalent 
rectangular pieces represent the cross section in the numerical 
integration procedure. The difference in the computed second moment of 
area, between the thin tubular section, approximated by rectangles and 
perfect thin tubular section is less than one percent (22). 






44 

4.6 Brief Description of the Solution Procedure 
A brief description, of the solution procedure outlined in Chapter 
6, is presented in this section to explain how the discrete element 
response is related to the overall frame response in the program 
FRAME82. The framed structure consists of members and joint shear 
panels. Each member is divided into a finite number of discrete 
elements which are then subdivided into several layers. Stiffness and 
End Force matrices of the discrete elements are obtained using the 
relationships in this and previous chapters. 

Member and joint solutions are performed separately to reduce 
computer time and to avoid large computer storage requirements. Each 
member is solved individually using as many elements as necessary to 
obtain each member's stiffness and fixed-end-force matrices. The ends 
of each member are "held" at the positions corresponding to the current 
joint displacements to obtain member solutions. Member stiffness and 
fixed-end-force matrices are computed using the discrete element tangent 
stiffness and fixed-end-force matrices, and standard matrix analysis 
techniques. The member and joint stiffness matrices are combined 
together to form the structural stiffness and load matrices. 

Since member and structure solutions are performed separately, an 
iterative cycle of each member occurs within each iteration on 
structural joint displacements. Special care needs to be taken to form 
correct stiffness matrix in the case of inelastic unloading. Tangent 
stiffness method used in this analysis to obtain nonlinear structural 
response is referred as Newton-Raphson method in mathematical numerical 
analysis. 



45 

4.7 Tangent Stiffness Method 
Consider a system of nonlinear equations of order n, given in 
Equation 4.47, which involves load vector P and displacement vector u. 
The vectors P and u represent the joint loads and displacements for 
joint solution, and member stations loads and displacements for member 
solution. 

P j = P j (u l' u 2> •'• u n ) j=l,2,...,n (4.47) 

Assume that {P} i and {u} i at the end of i th load increment are known 
and the above equation needs to be solved to obtain {u}. +l corresponding 
to {P} i+1 , the load vector at the end of (1+1) th load increment. 
Define {aP}. and {Au}. as 

^Ul = ^i + ^i (4.48) 

M i+ i ■ {u}. + {Au}. (4#49) 

Expand Equation 4.47 around {u} i using Taylor series: 



n 3P. 
P J " P J , i V., T5iif ( V Vi> J-l,2....n 



where 



k=l ou k 



J k,i j J=l,2,...n (4.50) 



P j,i = load p corresponding to j th degree of freedom at the 

end of 1 th load increment 
u k = displacement u corresponding to k th degree of freedom 
u kji ■ value of u k at the end of i th load increment. 

Terms in Equation 4.50 are rearranged to give the following 

relationship: 



n 3P. 

P H - P. - = AP.= E _i 

J a.i j k=1 su k 



;u}. (u k " u k,i) J=l»2,...,n (4.5i; 



In the matrix forr 






Hence, 



or 



{AP} = [K] {u} _{u - Uji } 

M (1) M u }^[Krj u}(?){ P, i+1 - P ,(o) } 

(AU}(°) = [K]" 1 {AP}(°) 

{u} ( ° } 



46 

(4.52) 

(4.53) 
(4.54) 



Matrix [K] represents the tangent stiffness matrix. Superscripts and 
1 denote the values at the beginning of the iteration and after the 
first iteration respectively. 

Since the Taylor expansion in Eq. 4.50 is curtailed after the first 
order derivative terms, {u} (1) obtained in Eq. 4.53 is the first 
approximation to {u}. +1 . Substitution of {u} i+1 in Eq. 4.47 will yield 
a load vector {P} which is generally different from {P} 1+1 . The 
difference' {aP} between {p}. +1 and P is commonly known as remnant or 
equilibrium error and defined as 

* AP > - i P l i+ l " (Pi (4.55) 

Successive iterations are required until this error is within the 

allowable tolerance. Repetition of iteration yields the following 
algorithm: 



and 



where 



M (n) ■ CK]- 1 (n) {AP} n 

{u} (n + 1 > ={u} (n) + {M<"> 



(4.56) 



(4.57) 



^ (R) ' H + l " W 00 (4.58) 

Superscripts n and (n+1) denote the values corresponding to the 
iterative cycles n and (n+1). 



47 

The above explained method is presented in References 46 and 56, 
and geometric interpretation of this procedure is given in Fig. 4.4 for 
a single degree of freedom system. The flow chart displayed in Fig. 4.5 
illustrates the procedure involved in the tangent stiffness method to 
solve a set of nonlinear equations. An integer is assigned to each 
stage of the flow chart and stage 4, which is intentionally excluded in 
this flow diagram, is introduced in the next section that considers the 
possibility of inelastic unloading. 

4.8 Modified Tangent Stiffness Method 
The above described tangent stiffness method in Section 4.7 needs 
to be modified to include the effects of strain reversal. A detailed 
description of the procedure demonstrated herein is given in Ref. 47. 
After computing the displacement vector in stage 3 of the flow chart in 
Fig. 4.5, one should not proceed to stage 5 during first iteration. 
Rather, compute the strains at each inelastic "component" such as 
subrectangles, joint shear panels, and member and joint support curves, 
corresponding to the incremented {u}. Check whether there is any strain 
reversal in any component. If none of the components undergo strain 
reversal, proceed to stage 5. 

If a strain reversal is sensed in any component, the entire 
procedure must be backed up. The history dependent slope of the stress- 
strain curve corresponding to the inelastic component, which sensed 
strain reversal, must be replaced with the largest slope of the stress- 
strain curve, the slope at the origin of the curve. The overall 
stiffness matrix thus obtained is referred to as "backed-up stiffness 
matrix." The displacement vector {u} must also be set back to the 
values prior to the strain reversal. This is symbolically represented 






48 




Figure 4.4 Tangent Stiffness Method (22' 












( start) 



49 



{API, - {P} i+1 - {p}. 




M = Mfjj {ap} 



{u} = {u} + {a u 



{P}-{P} M 



{ap} - {P} i+1 - P 



No 



/l AP k l < Tolerance for all k 



Yes 



H„-M 



Staae 



Figure 4.5 Flow Diagram for Tangent Stiffness Method 









50 



{u} = {u} + {a u } 







1st iteration j> 



No 



Yes 



M ■ {u} - {A U } 



Yes 



Strain Reversal in any 
structural component 



No 



(P) = {P} 



{u} 



Stage 

3 



Figure 4.6 Introduced New Stage in Modified Tangent Stiffness Method 



51 

as 

{u} = {u} - {Au} (4#59) 

Then the stages 1 through 7 are repeated except the formation of backed- 
up [K] and {u}, which is referred to as stage 4 in Fig. 4.6, until the 
solution converges or number of iterations exceeds the specified number 
of iterations. 
Strain Reversal Check 

The strain reversal can be directly determined for a single degree 
of freedom system by comparing the current load with the load history, 
without solving for incremental deformation. However, the above remark 
is not applicable to a general system with multiple degree of 
freedoms. Incremental displacements or deformations must be calculated 
to find out whether strain reversal has occurred in any subrectangle, 
joint shear panel or member and joint support curves. It is evident 
from the decomposition principle explained in Section 4.2 for a general 
nonlinear curve, that it is necessary to monitor only the first 
idealized elastic-plastic component to sense any strain reversal in the 
inelastic components. 






CHAPTER 5 
SHEAR BEHAVIOR AND STRENGTH OF STEEL JOINTS 

5.0 Introduction 



Structural frames are usually analyzed assuming that connections 
are rigid and the sizes of the connections are negligible. While both 
assumptions simplify the analysis, assuming rigid connection ignores the 
deformations at the joints and neglecting connection dimensions results 
in longer member length in the idealized frame than in the real frame, 
which in turn underestimates the member stiffnesses. In certain 
structures, the errors caused by the above cited assumptions may be 
self-compensating. However, in general, the size and the stiffness of 
the frame connections should be considered in the frame analysis to 
obtain rational results. 

In unbraced frames, structural stability and resistance to lateral 
loads require the transfer of bending moments between beams and 
columns. This transfer could be achieved by either semi-rigid or rigid 
beam-column connections. The beam-column joint will be subjected to 
high shears whenever a significant unbalance of beam moments is present 
at the joint. A significant unbalance usually exists at exterior and 
corner joints, and at the interior joints in the case of lateral load 
application such as wind or seismic effects. 

The shear design of joints is very important in frames that may be 
subjected to severe earthquake excitations. Such frames may experience 
stresses and deformations, which are very much higher than the values at 

52 



53 

service state. This imposes ductility requirements to be included in 
the design of frames to ensure serviceability of the structures. This 
chapter deals with various shear force-shear distortion relationships 
for joint behavior and the technique to incorporate joint shear behavior 
in the overall response of the structure. 

5.1 Shear Behavior of Joints 
The shear behavior of beam-column joints has been the subject of 
several experimental and analytical studies in recent years (3, 15, 31- 
35, 42-45). These studies concerned the monotonic and cyclic respbnses 
of all types of joints in general and interior joints in particular. 
Even though beam-column joints can develop failure due to one or 
combination of the factors such as column web crippling, column web 
buckling, column flange distortion, and shear yielding and shear 
buckling of the panel zone, only the shear failure mode of the joint 
panel is considered in this study. The material presented herein is 
obtained from references 32, 34, and 35. 

The following parameters listed below influence the joint behavior: 
(i ) Shearing resistance of the panel zone, which is a function of the 
panel aspect ratio d b /d c and the thickness of the shearing area, 
t cw + t s , where 

d c = distance between the centroids of the column flanges 
d b = distance between the centroids of the beam flanges 
t cw = web thickness 

t s = thickness of the shear reinforcement area parallel to 
the web 
(ii) Effectiveness of the shear reinforcement . 
(iii) Resistance of the structural components surrounding the panel 






54 

zone, which provides the post-elastic reserve strength of the 
joint. The flexural resistance of the column flanges and in- 
plane stiffness of the beam webs adjacent to the joint play major 
role. 

(iv) Type of connection 

(v) Beneficial effects of column shears - usually oppose the shear 
force produced in the joints by the beam moments. 

(vi) Effects of column axial loads, which must be included in the 

joint yield criterion. 
Several authors have investigated the influence of the parameters listed 
above on the behavior of joints. 

The most important characteristics of the joint behavior are 
summarized below. The shearing stresses are highest at the center of 
the joint panels with a moderate but definite drop towards all four 
corners. When the joints are stressed beyond the elastic limit, 
yielding in the panel propagates rather slowly from the center of the 
panel towards the level of beam flanges, for joints that have large 
aspect ratios (d b /d c ) and stiff column flanges. Joints with aspect 
ratio around unity and the column flanges thin and flexible, exhibit 
uniform yielding through out the panel. The distribution of shear 
deformations throughout a joint can be studied from the deformed shape 
of the joint, that is shown for a typical joint in Fig. 5.1 (32). 
References 32-34 reveal average shear strain and shear stress parameters 
of the panel, are adequate to model the joint behavior in the overall 
frame analysis. 

The shear stress-strain curve of a joint exhibits an elastic range, 
followed by a range of gradually decreasing stiffness, and then a strain 












55 




SI>lCiy£N 8-2 upij 



Figure 5.1 Deformations in an Interior Panel Zone (32) 




(a) SPECIMEN A-l 

Figure 5.2 Load-Deformation Diagram for a Joint (32) 



loom, mutts 




Figure 5.3 Effects of Excessive Joint Distortions (32; 



56 

hardening range with constant stiffness. The joint panel remains 
elastic until the panel zone yields, and in this elastic region, shear 
resistance is provided mainly by the shear panel. The transition range 
between elastic stiffness and strain hardening stiffness is governed, 
primarily by the elements surrounding the panel zone, particularly by 
the bending resistance of the column flanges and the in-plane stiffness 
of the beam webs adjacent to the joint. The strain hardening stiffness 
is largely attributed to the strain hardening in the material. 

Properly detailed joints exhibit a remarkable ductility and very 
stable and repetitive hysteresis loops under cyclic loading as displayed 
in Fig. 5.2 (32). No drop in strength is noticeable in such joints, 
even at extremely large inelastic distortions. However, under large 
distortions diagonal buckling might be observed in thin joint panels, 
and continued joint distortion would cause the formation of local kinks 
in beams and columns flanges, outside the joint, as illustrated in Fig. 
5.3, and could lead to the fracture of the material. The fracture would 
occur only after several load reversals at extremely large joint 
distortions. 

5.2 Shear Force-Shear Distorsion Relationships for Joints 
Krawinkler (32), Krawinkler et al . (34, 35) and Fielding (15) have 
recommended relationships to predict the behavior of joints based on 
their experimental investigations and analytical behavior of joints. 
Although the above authors utilized shear force and shear deformation, 
of the joint, as the parameters to describe the joint behavior, average 
shear stress and deformation are used in this presentation to be 
compatible with input stress-strain curves for members. An analytical 
joint shear stress-strain curve is derived from uniaxial stress-strain 



57 

curve and later modified to comply with the experimental observations 
made by the above two authors. 
5.2.1 Krawinkler Model 

The mathematical model used by Krawinkler to derive expressions to 
represent the joint behavior is displayed in Fig. 5.4. It consists of 
an ideal elastic-plastic shear panel surrounded by rigid boundaries with 
springs at the four corners. These springs simulate the resistance of 
the elements surrounding the panel zones, in particular the bending 
resistance of column flanges. 

The shear panel provides most of the resistance by shear 
deformations, until the average shear strain attains the yield shear 
strain. Thus, the joint shear stress in the elastic range is given by 

1 = Gy 0<y< Yy (5.1) 

where 

t = shear stress 
Y = shear strain 
G = shear modulus 

T 

Y = yield shear strain (= — JL) 
y /3G 

The increase in strength beyond t^ is attributed to the resistance 
of elements surrounding the panel zone, especially due to the flexural 
resistance of the column flanges. This resistance is represented by 
springs at four corners, whose stiffness is that corresponding to 
concentrated rotations of column flanges at each corner. When the 
boundary of the panel zones are assumed to be rigid, this spring 
stiffness is approximated by 






58 




k = G for < y < y 



for Y < Y < 4y 

y y 

G.u for 4y < y 
Sh y 



M 

= 



Eb t% 

— TD — l0r Y y < Y < % 

otherwise 



Figure 5.4 Mathematical Model for Joint by Krawinkler 







Gb t 2 
k* = 1.04 . c C T 

d b d c t 
= G sh = E sh /2 - 6 



■y 'y Y 

Figure 5.5 Krawinkler Model 



y 




n = 



n = 



62.4 l f 
d 



f\ 



15.6 x f 

g 



Y Y 

y m 

Figure 5.6 Fielding Model 



for interior and 
exterior joints 

for corner joints 






59 

, .M ^cf 
s F TO (5.2) 



The work equation gives 

d b AvA Y = 4MG (5#3) 



where 



and 



6 = Ay 



(5.4) 



AV = ATd c* (5.5) 

in which t = t w + t $ = equivalent thickness of the shear panel. In 
view of Equations 5.4 and 5.5, Equation 5.3 becomes 

— ■ 4M 

ay d b d c te (5.6) 

Feeding Eq. 5.2 into the above equation leads to 
Ax _ 4E Vcf 



Ay " 10d b d c t (5.7) 

Substitution of E = 2.6G in Eq. 5.7 gives the post-yield stiffness for 
the range Y <Y«4y 

At Gb t ^ ' 

i.e. ~ = 1.04 ^ CT ,, a^ 

Ay d b d c t (5.3) 

Even though the expression derived in Eq. 5.8 holds true only until 
yielding occurs in the column flange, the finite element study (34) 
showed that it is valid up to y - 4y y , the shear strain value at which 
the column flanges nearly attain their full plastic moment capacity. 
Hence, the joint shear stress is expressed as 






60 



Gb c t 2 f 
T = T y + U4 ^dV (y "V Y^-Ty (5.9) 



If the joint is strained beyond 4y strain hardening in the panel 
zone usually develops and the strain hardening stiffness is equivalent 
to E sh /2.6. Therefore, the joint shear stress can be written as 

Gb t\. E 



t + 3.12 cc f + sh 



y 



d^F- y y + ^ Y -%) ^>% (5.10) 



The joint shear stress-strain model recommended by Krawinkler is 
given in Fig. 5.5, along with the critical values. This model is 
expected to give good results for interior joints when the axial column 
load ratio P/P y is less than 0.50 and when the combined action of axial 
load and bending moment in the column will not cause yielding outside 
the joint, since early yielding of the column will decrease the 
resistance of elements surrounding the panel zone. This model is not 
applicable to corner joints which are bounded by framing elements only 
in two faces of the panel zone. When two beams of different depth frame 
into the column in interior joints, it is conservative to use the larger 
value of d b in joint stress calculations. 
5.2.2 Fielding Model 

Fielding and Chen (15) assumed a bilinear model shown in Fig. 5.6 
to represent the behavior of joint. Until the shear panel 
yields (y<Y y ), the shear panel deformation is assumed to provide the 
entire shear resistance, 
i.e. t = Gy <Y<Y ^ (5#u) 






61 

The strain-hardening stiffness of the inelastic region is obtained 
by considering the stiffness of the connection boundary elements (column 
flanges and horizontal stiffeners). These plate elements are assumed to 
bend in a frame type manner subsequent to softening of the shear panel 
due to shear yielding. In this range the deformation of the column web 
is assumed not to contribute to the additional connection capacity until 
strain hardening of the web begins. It has been found that flexural 
rigidity of the column flanges chiefly influences the load carrying 
capacity of webs in shear. 

The obtained post-yield stiffness parameter for interior and 
exterior connections is 



_ 62.4 l f 

n = ~Kr ~2 (5.12) 

s d 
9 

and for corner connections is 



_ 15.6 l f 

T7 (5 - 13) 

g 

where d g = girder depth; A s = effective shear area of the column web 
(product of the web thickness and the distance between flange 
centroids); and I f - the moment of inertia of the column flange. Thus, 



t - 1 h f 3 

l f " TTVcf (5.14) 



in which b c - column flange width; and t cf = column flange thickness. 

For the post-yield stiffness parameter n defined by Eqs. 5.12 and 
5.13 to be valid, the column web must not go into the strain hardening 



62 

region and the column flanges should not reach their full plastic moment 

capacities. Since it is found in experimental investigations carried 

out by Krawinkler (32) and Krawinkler et al . (34, 35) that the 

previously outlined conditions break down at y=4y , it is reasonable to 

assume that the model recommended by Fielding holds qood up to y =4y 

r m 'y' 

where Y m = maximum average shear deformation. 
5.2.3 Modified Analytical Model 

Analytical derivation of joint shear stress-strain curve from 
uniaxial stress-strain curve, described herein, yields a new model. 
Since this model does not include the resistance provided by the 
structural elements surrounding the joint panel zone, it has to be 
modified for the shear strain range Y y <Y«4 Yy to obtain a better model 
that would predict good results. The stiffness recommended by either 
Krawinkler or Fielding can be used in the range y <y<4y , where the 
column flanges offer a significant contribution, to modify the 
analytical model. 
Derivation of t-y Curve from c-e Curve 

Consider a general uniaxial stress-strain curve given in Fig. 
5.7 (a) to obtain the joint shear stress-strain curve. Levy-Mises yield 
criterion and the isotropic-hardening Levy-Mises theory described in 
Ref. 37 are used to obtain the required relationship. No distinction is 
made between natural and nominal strains in this derivation since the 
strain is assumed small . 

Mises yield criterion is given by 

J 2 = k (5.15a) 

or 

7 CT ij a i'j =k2 (5.15b) 



63 




(a) Uniaxial Stress-Strain 
Curve 



o 4 



y 



U P ,a) 



e P (- « - . y ) 

(b) Uniaxial Stress-Plastic 
Strain Curve 



(/3 e P,a//3; 



(c) Shear Stress-Plastic Strain Curve 



T " 



( Y +/3 £ P ,a//3) 




(d) Shear Stress-Strain Curve 



Figure 5.7 Graphical Representation of the Derivation of Shear Stress- 
Strain Curve from Uniaxial Stress-Strain Curve 



64 

where J£ = second invariant of the deviatoric stress tensor- a 1 = 
deviatoric stress on the plane i along the direction j; k = a constant. 
Deviatoric stress a!, is defined as 

°ij = a ij" p6 ij (5.16) 

where a.. = stress; and p = mean normal stress and given by 

(a ll + a 22 + a 33 } 



P ■ 



(5.17) 



Eq. 5.15b can be rewritten as 

J 2 = k2 = -6^ a ir°2 2 ) 2 + ^ 22 -°33) 2 + ^S^ll^ + a 23 + 4l + A 



2 

(5.is: 



For uniaxial stress c n , the space is one dimensional and the condition 
defining the yield surface is given by 

|a lll = a y (5.19) 

Substitution of Eq. 5.19 into Eq. 5.18 leads to 

a 2 
k2 = F (2a y } =J 5 (5.20) 



For pure shear in the xy plane, a u = o n - x y and the rest of the a. -s 
are zero. Substitute these conditions into Eq. 5.18 and obtain 

k 2 = t 2 

k T y (5.21) 

In view of Eq. 5.20 and 5.21, the yield shear stress is 

T y = V /3 (5.22) 

and the corresponding yield shear strain is 

T y " V G (5.23) 



65 

Isotropic hardening assumption, that the yield surface maintains 
its shape, while its size increase is controlled by a single parameter 
depending on the plastic deformation, is used to obtain the shear 
stress-strain curve in the inelastic region. The universal plastic 
stress-strain curve defined by two scalar quantities, the effective 
stress a and the integral of the effective plastic-strain increment 
d£ p , governs the yield surface. When used with the Mises yield 
condition, the appropriate effective stress 5 is 

5 ■ /S3J - l^:,:.f . ^(a n -a 22 ) 2 ♦ ( 022 -a 3 3) 2 ♦ f^-^) 2 } 



1 

23 " °31 r a 12 JJ (5.24) 



+ 3(4 + ol + a? 9 )]2 



and the appropriate effective strain increment de to use with a is 

r 

i i 

+ (deP 2 -d £ P3) 2 + (deP3-d e P 1 ) 2 } + 4j(d e P 3 ) 2 

1 

* Cd«§! ) 2 + (d £ p 12 ) 2 }] 2 (5.25) 

where n d£ p = second invariant of the plastic strain increment tensor. 

For uniaxial stress a n , all the stress components are zero other 
than a n . Hence, the effective stress defined in Eq. 5.24 becomes 

° = CT 11 (5.26) 

Plastic incompressibility implies the following condition: 



66 



deP = deP. = - i deP 



22 ~ ut 33 " " 7 QE U (5.27) 

Substitution of Eq. 5.27 in Eq. 5.25 yields the effective plastic strain 
increment as 

d£ "p = d£ ll (5.28) 

For pure shear in the xy plane, all the stress components other 

than a 12 and a n , and all the strain increment components other 

than e { 2 and eP^ are zero. Hence, Eqs. 5.24 and 5.25 give the effective 

stress and plastic strain increment in the following expressions: 

5=/3a 12 (5.29) 

p "73 d£ 12 = ^J- (5.30) 

Equations 5.26 and 5.29, and 5.28 and 5.30 provide the required 
relationships between uniaxial and sher stress-strain curves in the 
inelastic region, 
i.e. a 12 = 7J o n (5>31) 



and d Y P 2 = /3d,P 1 (5>32) 



The slope of the shear stress-strain curve in the inelastic region is 
obtained from the above two equations as 

dq 12 _ 1 dq ll 

dyf 2 " 3 d«5 2 (5 ' 33) 

Equations 5.22 and 5.23, and 5.33 are used to obtain the shear stress- 
strain curve in the linear elastic and inelastic regions respectively. 



67 



lib t ~- 

(4 V T y + >12 w' 




d: „ 1 do 
dY 3 d£ 




(a) Analytical Curve with Krawinkler Recommendations 



T '• 



(4y y5 T*) 





dr B 1 do 

dy 3 de 



t* = t (1 + -j— : __) for interior joints 

y s d^ 



T ,. . 46.8 l f v - . . . 
t (1 + — t 5—) for corner joints 

y s <T 
9 



(b) Analytical Curve with Fielding Recommendations 



Figure 5.8 Analytical Shear Stress-Strain Models for Joints 









68 

Figure 5.7 (b) shows the uniaxial stress versus plastic strain (strain- 
yield strain) curve. Stress ordinates are shrunk by a factor of /3, 
while plastic strain abscissae are stretched by /3 to obtain the shear 
stress-plastic shear strain curve in Fig. 5.7 (c). Linear elastic 
segment of the shear stress-strain curve is added to Fig. 5.7 (c) to 
derive Fig. 5.7 (d), the analytical shear stress-strain curve. 

The shear stress-strain curve of the web (and stiffeners) can be 
derived from its uniaxial stress-strain curve. This has to be modified 
to include the effects of elements around the panel zone in the shear 
strain range, Yy to 4y y . This could be achieved by using the 
relationships suggested by Krawinkler and Fielding in the above 
mentioned range. It is worthwhile to note that elastic shear strain 
curve is the same for all the models that are discussed in this chapter, 
including the analytical model. Therefore, no matter whose model is 
employed to include the effects of elements surrounding the panel zone, 
the difference from the particular model would be only in the strain 
hardening region beyond 4 Yy . The modified analytical models 
corresponding to Krawinkler and Fielding models are displayed in Figs. 
5.8 (a) and 5.8 (b). It is interesting to observe that Krawinkler model 
uses 2.6 instead of 3.0 used in the modified analytical model, in the 
strain hardening range beyond 4y . 

5.3 Four Degree of Freedom Joint Stiffness Matrix 
The shear strain y xy at any point in a solid continuum is given by 



3u 9u v 
xy " V 3T" + 3lT j (5.34) 



where (u x , u y ) are displacement components of the point parallel to the 



69 



X and Y axes. Consider the deformation shape of a rectangular panel 
subjected to pure shear deformation in Fig. 5.9 (a). The rotations 8 X 
and 6 2 of the fibers parallel to x and y axes are defined by 

3u 

6 = — i 

1 3X (5.35a) 

3u 

a _ X 



2 3Y , (5.35b) 

Hence, y xy - ^ ^ 2 (5<35c) 

For pure shear deformation 

9 1 = 9 2 (5.36) 

Figure 5.9 (b) displays a rectangular panel that is undergoing a pure 

rigid body motion. Any fiber in the panel is rotated by the same 
angular movement. 

1,e * 6 1 = 9 2 (5.37) 

Note that % 2 is defined in opposite directions in Figs. 5.9 (a) and (b) 
for convenience. 

It is imperative to include an additional degree of freedom for 
each joint, to the generally used three degrees of freedoms, namely 
horizontal, vertical, and rotational displacements, to incorporate the 
joint shear deformation in the frame analysis. Transl ational 
displacements of the geometric centroid of the shear panel along the x, 
y directions and rotational displacements of both x, y axes are chosen 
as the four degrees of freedom in this study. The following assumptions 
are necessary to simplify the analysis, 
(i) Shear panel is of rectangular shape with constant thickness and 

its edges are parallel to the x, y axes before being stressed. 






70 



All. 



AY 




(a) Pure Shear Deformation with 
No Rigid Body Rotation 




(b) Rigid Body Rotation 



Figure 5.9 Shear Deformation and Rigid Body. Rotation of a Rectangular 
Shear Panel 



y 


1 






e 








V 








y * 




f 2 




G 


— *■ 


) 




u 


/ 


X 


X 








i = e - 9 

S Z V 

) = (8 +6 
r z v 



)/2 



(a) Undeformed Panel 



(b) Deformed Panel 



Figure 5.10 Rectangular Shear Panel with Four Degrees of Freedom 



71 

(II) Shear panel experiences a constant-shear-flow distribution. 

(III) Joint may undergo large rotations, but the deformation, or change 
in rotation, is small . 

First, a four degree of freedom stiffness matrix is derived for a 
rectangular joint shear panel of constant modulus of rigidity and later, 
it is modified to include the inelastic behavior of the shear panel. 

Constant shear flow distribution assumption implies that the 
geometry of any point within the shear panel can be defined in terms of 
the selected four degrees of freedom at the geometric centroid of the 
panel. The chosen degrees of freedom u x , u y , 9 z and 6 y , which denote x- 
displacement, y-displacement, x-axis rotation, and y-axis rotation 
respectively, are shown in Fig. 5.10. Let the respective forces be f 
f y , m z , and m y , where the moments m z and m y represent the couples 
produced by the shear forces along the edges perpendicular to x and y 
axes respectively. These moments are equal and opposite in direction, 
for a shear panel undergoing pure rigid body motion. The rigid body 
rotation of the shear panel corresponding to any deformation is 
displayed in dashed lines through the lower most corner of the panel to 
define rigid body rotation 6 p and shear deformation 8 g in terms 
of 8 z and e . 

Application of Eq. 5.36 to the deformed rectangular shear panel in 

Fig. 5.10 gives the following relationship. 

9,-0 = e - e 
z r r. v 

i.e. 

9 r " < 9 z + 9 v)/2 (5.38) 

Similarly, application of Eq. 5.35c leads to 

9 s = ( 8 z - 9 p) + ( 9 r - V 



72 



i .e. 



' = ( 9 
s v z 



,) 



(5.39) 



Linear Elastic Joint Shear Stiffness Matrix 

The elastic joint stiffness matrix [k], joint forces {f}, and 
displacements {w} are related to each other by the following equation: 

( f l ■ DOM (5>40) 

where 



{f}t =[ V V V%3 
M* - C V V V V 



(5.41) 
(5.42) 

















[k] = Gabt 






















1 


-1 










-1 


1 



(5.43) 



in which G = elastic shear modulus; a = undeformed length of the shear 
panel parallel to x axis; b = undeformed length of the shear panel 
parallel to y axis; t = undeformed thickness of the shear panel. 
Incremental Joint Shear Stiffness Matrix 

Incremental joint stiffness matrix [k] is related to the 
incremental joint force vector {df} and incremental displacement 
vector {dw} by the following expression: 

{df} = [k]{dw} 
where 

{df}* = [df , df , dm . dm ] 



(5.44) 



y* z 

{dw}* = [du x , du , de z , dO y ] 



(5.45; 
(5.46; 









73 



[k] = G t abt 

































1 


-1 








-1 


1 



(5.47) 



J 



in which G t = slope of the joint shear stress-strain curve at the 
current deformed configuration. 

5.4 Member Stiffness Matrix in Four Degree of 
hreedom Structural Coordinates 

Since the joint stiffness matrix is associated with four degrees of 
freedom, it is required to transform the member stiffness matrix 
formulated in three degree of freedom structural coordinate system into 
four degree of freedom structural coordinate system to include joint 
deformation effects in the analysis. Thus, a member stiffness matrix of 
order 6X6 would become an 8X8 member stiffness matrix. A member 
stiffness matrix can be written as 



DO 



Ck n ] [k 12 ] 
Dc 21 ] [k 22 ] 



(5.48) 



where the suffixes 1, 2 in the submatrices represent the to and from 
joints. The order of each square submatrix is equal to the number of 
degrees of freedom. If the transformation matrices are known at the to 
and from ends, then the submatrices of the transformed stiffness matrix 
can be obtained using the following transformation relationship (56): 

^1? ce T o [TO 



» H 3 



4X4 



' J 4X3 ''" IJ 3X3 L ' J 3X4 



'5.49' 



where [T] is the transformation matrix and I, J could represent either 



74 

from or to ends of the member. It is to be remembered that [T] relates 
the three degree of freedom member displacements {w} to the four degree 
of freedom joint displacements {w} as given in Eq. 5.50: 

{dw} 3X1 - [T] 3X4 {dw} 4xl (5<50) 

As the joint stiffness matrix is known only for the rectangular 
panel, the present analysis is restricted to rectangular frames with no 
diagonal bracings. The required transformation matrices are derived 
herein for both horizontal and vertical member ends. 
Transformation Matrices 

Transformation matrices need to be derived for four cases, namely 
shear panel at the from end of horizontal member, shear panel at the to 
end of horizontal member, shear panel at the from end of vertical 
member, and shear panel at the to end of vertical member. The 
dimensions of the rectangular panel used are given in Fig. 5.11 ( a ). 
Figure 5.11 (b) is considered for the derivation of transfer matrices 
for horizontal and vertical members. Since the derivation of transfer 
matrices is very similar for all four cases detailed derivation is 
provided only for the case of shear panel at the from end of horizontal 
member. However, the transfer matrices of other cases are also listed 
herein. 

Consider the joint shear panel and horizontal member at the right 
in Fig. 5.11 (b) to obtain the relationship between member displace- 
ments {w} and joint displacements {w} for the case of shear panel at the 
from end of horizontal member , where 

{«}* ■ [u A , v A , e A ] (5>5l) 

{w}t = C V V V V (5.52) 

From geometry 



75 



(a) Dimensions 




(b) Shear Panel and Member End Displacements 



Figure 5.11 Rectangular Shear Panel 



76 



u A - u + h cos 



(5.53a) 

v A = u + li sin 8 ,r (-, k \ 

A y r z (5.53b) 

6 A = 9 v (5.53c) 

where, h p = horizontal distance of the right vertical edge from the 

Differentiation of the set of 



geometric centroid of the panel 
equations in Eqs. 5.53 yields 

du A = du x - h p sin Q z d6 z 

dv 



'A 



du + h p cos 8 de 



de. = de 

A v 



Hence, the transformation matrix [T] is given by 



(5.54a) 
(5.54b) 
(5.54c) 



[T] 



1 -h r sin8 z 



1 h r cos8 z 







(5.55) 



The transformation matrix for the case of shear panel at the to end of 
horizontal member is given by 



[T] = 



1 h £ sin8 z 

1 -h.cose 
& z 

1 



(5.56) 



where h g - horizontal distance of the left vertical edge from the 
centroid of the panel . 

The transformation matrix for the case of shear panel at the from 
end of vertical member is given by 



77 



[T] = 



1 -V.COS0 
t v 

1 -v.sine 
t v 

1 



(5.57) 



where v t = vertical distance of the top horizontal edge from the 
centroid of the panel. 

The transformation matrix for the case of shear panel at the to end 
of vertical member is given by 



[T] = 



1 v K cos9 
b v 

1 v.sine 
b v 

1 



(5.58) 



where v b = vertical distance of the bottom horizontal edge from the 
centroid of the panel. 

5.5 General Comments on DRAIN 2D Analysis 
DRAIN 2D, the program developed by Kanaan and Powell (30), also 
uses a constant shear-flow infill panel element to incorporate the 
effects of joint shear deformation in the analysis. The element is 
assumed either rectangle or very close to a rectangle in shape. 
Flexural and axial deformations are ignored in the analysis. The infill 
panel element is treated as an isoparametric finite element with eight 
degrees of freedom, two translational degrees of freedom at the center 
of each boundary. The infill panel element is connected to beam-column 
members at nodes. In general, the infill panel element would have four 
nodes. A beam-column member has two nodes (one at each end) with three 
degrees of freedom (two translational, one rotational) per node. 



78 



Large displacement effects which are included in the FRAME82 
analysis, are not taken into account in the DRAIN 2D analysis. The 
effect of semi-rigid connection element incorporated in the DRAIN 2D 
analysis can be obtained by inputting a proper joint shear stress-strain 
curve in FRAME82 analysis. 






CHAPTER 6 
FRAME ANALYSIS 

6.1 Assumptions 
The following assumptions are made to derive the theory used in the 
development of the program FRAME82: 

(1) Plane frame - displacements and forces are in the plane of the 
frame. 

(2) The deformations (strains and curvature) are of an infinitesimal 
order, though the displacements (axial, lateral and rotational) can 
be finite and large. 

(3) Linear strain distribution across the depth of a cross section. 

(4) Member shear strain is in the linear eleastic range. No 
interaction between shear strain, and axial and flexural strains is 
considered for members in the strain hardening region. 

(5) Shear deformations of joint is included - axial and flexural 
deformations are neglected. 

(6) A general stress-strain curve is assumed for member flexural and 
joint shear curves. 

(7) First assumption implies that out-of-plane buckling cannot be 
considered. Local buckling of flanges and web is also not 
included. 

(8) In a dynamic analysis, masses are lumped at the structural joints. 

(9) Acceleration is constant within each time step since constant 
average acceleration method is employed. 

79 



80 

(10) Mass and stiffness dependent damping is assumed. 

(11) Residual stresses are not included in the analysis. 

6.2 Outline of the Solution Procedure 
The structure is idealized as an assemblage of members and joint 
shear panels. Each joint (node) possesses either three or four degrees 
of freedom depending on whether the joint shear deformations are 
included or ignored. The analysis that includes joint shear 
deformations utilizes an additional rotational degree of freedom per 
node, as explained in Chapter 5, to include the effects of shear 
deformations. Each member is divided into a finite number of discrete 
elements. Thus, any variation in member properties, loading or 
restraints may be represented. Each discrete element is subdivided into 
several layers to compute the discrete element stiffness and fixed end 
matrices, derived in Chapters 3 and 4. Subdivision helps to include 
variation in geometric properties of the section and in stress at 
different levels across the depth of the section. Member loads and 
restraints are discretized to the member station points. Static loads 
can be applied anywhere in the frame, but dynamic loads must be applied 
only at the joints to simplify the dynamic analysis. 

It is not economical to solve for member station and joint 
displacements simultaneously, since the procedure includes a large 
system of equations, that has a large bandwidth and requires large 
computer storage and time. Therefore, member and joint solutions are 
performed separately to reduce the computer cost. Individual members 
are solved separately using desired number of discrete elements to 
obtain member stiffness and fixed-end-force matrices. The relationships 
between member end displacements and joint displacements, presented in 



81 

Chapter 5, are used to obtain the above matrices in the structural 
coordinates. The transformed matrices are then assembled to form the 
overall structure stiffness and load matrices, to solve for either joint 
displacements or joint displacement increments depending on linear or 
nonlinear analysis. 

Since member and joint solutions are performed separately, an 
iterative cycle for each member occurs within each iteration of the 
joint solution. The member ends are "held" at positions corresponding 
to the current joint displacements to obtain member solutions. Thus, 
the procedure updates the structure stiffness after each iteration, and 
adds any unbalance in equilibrium as a corrective load. 

The dynamic analysis presented in this chapter is valid for a 
general coupled mass matrix. However, the program considers only a 
diagonal mass matrix, and ignores the inertia masses. If desired, the 
program could be easily modified to consider coupled mass matrices. 
Although mass and stiffness dependent viscous damping is used in the 
theory, only mass dependent damping is incorporated into the program 
FRAME82. 

Joint equations are set up including the tributary masses and 
viscous damping to obtain the governing structure dynamic equations, 
whereas member equations are concerned only with the static equilibrium 
of the members. Numerical integration of the coupled equations of 
motion is carried out using constant average acceleration method. 
Iteration is performed within each time step until the equilibrium 
errors are within the specified tolerences. Equilibrium errors are 
applied as corrective loads in the subsequent iteration. 



82 

6.3 Dynamic Analysis 
The governing frame (joint) differential equation of motion is 
derived herein (4, 10, 11, 30). At any instant of time t, an equation 
of dynamic equilibrium can be written as 

(Fl(t)} + {F D (t)J + (F s (t)} = {F(t)} (6.1) 

in which F(t) is the nodal (joint) force vector; Fj(t), F D (t), and F s (t) 
are the forces due to inertia, damping, and stiffness respectively. A 
short time At later the equation would be 

{F^t+At)} + (F D (t+At)} + {F s (t+At)} = (F(t+At)} (6.2) 

Subtracting Eq. 6.1 from Eq. 6.2 yields the incremental form of the 
equation of motion at time t as 

{AFj(t)} + (AF D (t)} + {AF s (t)} = {AF(t)| (6.3) 

The incremental forces in this equation may be expressed as 

{AFj(t)} - {Fj(t+At) - Fj(t)} - [M]{AW(t)} (6.4a) 

{AF D (t)j = (F D (t+At) - F D (t)} = [C T (t)]{AW(t)} (6.4b) 

(AF s (t) = {F s (t+At) - F s (t)} = [K T (t)]{AW(t)} (6.4c) 

where [M] is the mass matrix that does not change with time, and [C T (t)] 
and [K T (t)] are the tangent damping and stiffness matrices. The 
elements of the incremental damping and stiffness matrices are influence 
coefficients C Tij -(t) and K Tij -(t), and are given by 

. r 3F Di 

Tij'^r (6 - 5a) 

J 
3F C . 
Tij ^¥7 (6.5b) 

•J 

When Eqs. 6.4 are substituted into Eq . 3, the incremental equation of 
motion becomes 






83 

[M]{AW(t)}+[C T (t)]{AW(t)}+[K T (t)]{AW(t)} = (AF(t)} (6.6) 
Rewriting Eq. 6.6 for a time step j leads to 

CM]{AW}. + LCj^m. + [K T ]. {AW}. - {AF}. ( 6 . 7 ) 

It is to be reminded that Eq. 6.7 is an approximate equation because of 
the use of initial tangent values for damping and stiffness terms. 

The constant average acceleration method is used to solve the 
incremental differential Eq. 6.7. The basic equations for this method 
are presented in Appendix B. It is assumed that viscous damping results 
from a combination of mass dependent and stiffness dependent effects, so 
that 

[C T ] = a[M] + 3[K T ] (6<8) 

in which a and are constants to be chosen depending on the damping 
characteristics of the structure. 

Using the equations given in Appendix B to relate incremental 
acceleration and velocity with incremental displacement, Eq. 6.7 can be 
written as 

[M]{-2W . ^.w f-i^AW} + [a[M]+6CK T ]J{-ZiJ,+ It AW} 
J L J ^ ' J J At J 

+ [KyljfAW} = {AF}.. 
i .e. 

[(^ + ^)[M] + (|f + i)[K T ].]{ia}. . 

{AF}. + [M]{2ii. t^llj + 2aW.} ♦ 2B£K T ] J {flf J ( 6 . 9) 

Equation 6.9 can therefore be written as 

[y[MMK T ] j ]{AW} j = {AF} j+ [M]{2W j ^ j+ 2aW j -23 Y W j } (6.10) 



l .e. 



{Afl} j =[T[M] + [K T ] j ]- 1 {{AF}. + [M]{2W. + (| r+ 2a-23y )>;/.}} (6.11) 



where y - (^ + f£) I (|f + 1) (6 . 12 ; 



84 
and {AWlj = 1 {Afl. +20ft J (6a3) 



At 



Once {AR}. has been determined by Eq. 6.11, the increment of nodal 
displacement {aw}, follows from Eq. 6.13, and the incremental velocity 
and acceleration follow from Eqs. B.5 and B.6 respectively. 

6.4 Dynamic Equilibrium Check 
Due to nonlinear nature of the response, unbalance forces may exist 
at any joint after predicting {aW}.. and computing the inertia, damping 
and member forces corresponding to the new displacement' {W} These 
unbalanced forces or "equilibrium" errors should be successively 
corrected until they are within specified tolerance in order to predict 
displacements, velocities, and accelerations for the next time step. 

The dynamic equilibrium error {E} j+1 at the j+1 th time station 
results from the lack of satisfaction of equations of motion. Thus, 
from Eq. 6.2 

H-h-1 = H- + 1 " ( F lVl " ^ F s)j + l - iF D } j+1 (6.14) 

All the components on the right hand side of Eq. 6.14 can be exactly 
computed except {F D } j+1 which is the damping force. However, it can be 
calculated to a fairly reasonable accuracy by integrating the following 
tensor equation: 

8F Di 
dF D . =^r 1 dW. (6a5) 

J 

In matrix notation the above equation can be written as 

{dF D } - [C T ] {dW} (6ag) 

Therefore, 



85 

{F D 1 ={F D }_ + / [C T ]{dW} (6J7) 

J 

To evaluate the integral in Eq. 6.17 use the average value over the time 
interval for [C T ], In other words, a parabolic distribution is assumed 
for damping force within a time step. Then Eq. 6.17 becomes as 

V = ^uK + Y [ a M + 3CK] +a[M] + 3[K] ]{AW} (6.18a) 



i .e. 



{f d^. +1 = i^l* [«CM3 +|CCK] j+ [K] j+1 ]]{W-Q.} (6 .i 8b) 

where {w} is the current value of the predicted velocity vector. 

The dynamic equilibrium error {E} j+1 can be considered as an 
additional force not absorbed by the system. If this error is applied 
to the system before proceeding to the next time step, then 

Mj ■ [YCM] + [K,]]" 1 ^ (6 . 19a) 



l .e. 



{aw}. . i [ y[m] + [Kt]] -i {e) 2 (6>19b) 

At 

where [K T ] varies during the time step. This {aw}, has to be added to 
the previous estimate of {w} j+1 . This displacement increment 
of {AW}., will also cause increments in velocities and accelerations, and 
they are given in Eqs. 6.20 and 6.21: 

Wj -If^Jj (6.20) 

(AWlj -^{AW}j (6 . 21) 

The above equations are obtained by omitting the terms {w}. and {*W}. in 

J J 
Equations B.5 and B.6, since their contributions have already been 

included in the first iteration. 



86 

Now the latest estimate of displacements, velocities, and 
accelerations can be computed and checked for the dynamic equilibrium 
again. If the dynamic equilibrium errors from Eq. 6.14 are sufficiently 
small, then the solution proceeds to the next time step. Otherwise, it 
is necessary to perform more iterations within the time step. 

6.5 Damping Constants 

The following procedure can be used to select the damping constants 
a and e. The relationship between generalized damping c n , and 
frequency cu n , of a linear elastic structure is given by (4, 10) 

CC n ] = «Dl n ] + 3[K n ] (6<22) 

in which, suffix n dentoes the nth mode and 



[C n^ ' ^Vy ( 6 . 2 3 a ) 



and 



[K n ] = CVfr (6.23b) 

where ? n = a proportion of critical damping in the n th mode. In view of 
Eqs. 6.23, Eq. 6.22 can be written as 



? n = l [ ;r + e«n 3 (6.24) 

The advantage of this definition of damping should be apparent, because 
it clearly shows that stiffness dependent damping is more effective in 
the higher modes, whereas mass dependent damping controls the motion in 
the lower modes. The damping constants a and 3 can be defined in terms 
of proportion of critical damping £, and circular frequency oo, at two 
differnent modes as expressed below. 

j r 



87 



,2 2, (6.26) 

(01. - <d. ) ' 

For practical analysis, u. and 5 may be obtained for two different modes 

corresponding to the elastic structure and then values of a and e can be 

determined from Eqs. 6.25 and 6.26. 

6.6 Comparison with Other Methods 
In the above described method, the tangent value of damping is 

assumed as a linear combination of mass and tangent stiffness 
matrices. The damping force is then obtained by integrating the tangent 
damping matrix with respect to velocity vector. A parabolic 
distribution is assumed within a time step to evaluate the integration. 

Kanaan and Powell (30) also assumed the damping matrix as a linear 
combination of mass and tangent stiffness matrices. But they assumed 
the incremental damping force as [C y ]{AW}, which is not necessarily true 
in the case of nonlinear structures. It is true only for linear elastic 
and nonlinear structures with tangent damping independent of 
stiffness. The preceeding statement is justified by Eqs. 6.27 defined 
below: 

{AF c } = [C T ] {AW} + [AC T ] {ft} (6>27a) 

i.e. 

{AF c } - [C T ] {AW} + B[AK T ] {W} (6#27b) 

The procedure adopted by Kanaan and Powell did not include the second 
component on the right hand side of Eq. 6.27b. This means an additional 
load equivalent to 3[AK T ]{W} was permitted to act on the structure, 
which may significantly modify the resulting response of the 
structure. Therefore, an equal and opposite load of 



88 

magnitude -g[AK T ]{w} must be applied as a corrective load during the 
subsequent time step. The analysis described herein includes th 
contribution due to change in stiffness while evaluating the damping 
force by Eq. 3.18b during each iteration. It is also to be pointed out 
that their analysis used neither dynamic equilibrium check nor iteration 
within a time step. 

6.7 Comment on Static Analysis 
The solution for static analysis utilized exactly the same 
procedure that is outlined for the dynamic analysis. However, the 
absence of damping and inertia terms in the static equlibrium equations 
simplify the analysis and procedure is explained in Section 4.7 under 
tangent stiffness method. 



e 



CHAPTER 7 
THE COMPUTER PROGRAM FRAME82 

7.0 Introduction 



The computer program FRAME82 is developed for the inelastic 
analysis of plane frames under static and dynamic loadings and is 
subjected to the restraints outlined in Chapter 6. It is the latest 
enhanced version of the earlier programs FRAME63 of Santhanam (47) and 
FRAME53 of Hays (22). In addition to the important features such as 
nonlinear geometry, inelastic material, and member and joint supports, 
and cyclic loading available in FRAME63, FRAME82 includes member and 
joint shear deformations and mass dependent damping. The program is 
written in FORTRAN IV language for the 1MB 370 Computer. Minor 
modifications may be needed to install this program on a different 
system. 

Input Guide for FRAME82 and the required JCL statements to perform 
FRAME82 analysis on an IBM 370 system are given in Appendices C and D, 
respectively. Appendix E contains a glossary of the FORTRAN variables 
used in the program FRAME82, and is followed by a complete listing of 
the program in Appendix F. Several comment statements are inserted in 
the program to facilitate the understanding of the program logic. 
Sample inputs and a sample output are listed in Appendices G and H, 
respectively. 



89 



90 

7.1 Main Features and Limitations of FRAME82 

1. Dimensions: The program is presently dimensioned to analyze a 
frame of 25 joints, 50 members, 20 cross sections, 20 elements per 
member, etc. The MAIN program of FRAME82 consists of a dimension guide 
to make modifications in the dimensions of the program. 

2. Discrete Element Model Type : Either shear or flexural discrete 
element models can be specified for each member. Shear model includes 
the effects of member shear deformations, that is ignored by the 
flexural model, in the member stiffness matrix formulation. 

3. Number of Discrete Elements : User can specify different number 
of elements for each member, depending on its length and loading 
conditions, to obtain the desired accuracy. Almost double the number of 
shear elements are required to obtain the same accuracy for flexural 
response as of flexural analysis. This point is discussed in detail in 
Chapter 8. The number of elements for each member must be between four 
and twenty. 

4. PDNO option : Usage of PDNO option ignores P-A and P-y moments 
and a completely linear geometric analysis is performed. 

5. JSYES option: This sets the program to incorporate the effects 
of joint shear deformations in the analysis. Since the joint model was 
developed only for a rectangular joint, this option can be specified 
only for rectangular frames. 

6. Member Flexural Stress-Strain Models : The flexural stress- 
strain behavior can be prescribed to be linear elastic, nonlinear 
elastic, Masing inelasticity, Masing inelasticity with stiffness 
degradation or special model for mild steel, as listed in Table 7.1. 
Flexural discrete element model is verified for all the above described 






Table 7.1 Stress-Strain Models (48) 



91 



Type and a—* path 
(1) 



Linear 
elastic 



Nonlinear 
elastic 



Masing 
component 



Degradation 
component 
(proposed) 




Degradation 
factor, a 

(2) 




0.0 



J "-7" 




£ a £ 1 

(a = 0, Ref. 21) 

(a = I, Ref. 5) 



a (40 

(suggested 
range is 
0.15-0.30) 



"Region parameter — kl = positive yield; ■■ 
Reversal parameter — = no; 1 = yes. 



Yield 
growth 
factor, 3 

(3) 



0,0 



0.0 



3 /o 

(suggested 
range is 
0.3-0.6) 



Memory Parameters 



For 
each 
com- 
ponent 
(4) 



For first 

component 

(5) 



region 
reversal" 



region 
reversal 



Only One Component 



region 
reversal 



.ro-„ 



elastic; -1 



negative yield— all first component. 
ofan 0t a e nai U s.r SCriP ' S "* "^ '''' "'" * ^^ *""" ™ d in in "™ d -° iMta. 












92 

five types of stress-strain models. However, the shear discrete element 
model is verified only for the first three, namely, linear elastic, 
nonlinear elastic, and Masing inelasticity stress-strain models. 

7. Member Shear: Input modulus of rigidity and specify discrete 
shear element model, for a member type to include member shear 
deformations into the analysis. The program considers only the linear 
elastic shear deformations. 

Jb Joint Stress-Strain Curves : The analytical joint model 

considers only the joint shear deformations and neglects flexural and 
axial deformations. Linear elastic or inelastic of Masing type can be 
prescribed for the joint shear stress-strain curve. Thus, any of the 
joint shear models described in Chapter 5 may be used in the analysis. 

9. Joint and Member Supports : Either linear elastic or Masing 
inelastic stress-strain curves can be specified for joint and member 
supports. 

10. Viscous Damping : Mass dependent damping can be prescribed to 
include viscous damping in the dynamic analysis. 

11. Analys is Restart Feature : Provisions are available to pick up 
the results at a particular loading stage and proceed the analysis from 
that stage. This enables the user to break an analysis of a structure 
that would take a huge computational time, into several runs, and also 
helps the user to reduce time and load increments in the vicinity of 
load reversal regions where ill-condition exists for the stiffness 
matrices. The input guide of Appendic C explains the details for 
performing continuation runs. 



93 

12. Automatic Load Reduction of Static Loads : In case of a 
solution failure, automatic load reduction feature allows the program to 
reduce the static joint and member loads by specified percentages and to 
start a fresh analysis from the last available good solution. User must 
prescribe the number of such load reductions. Provision is also 
available to prevent any decrease or increase on the desired member 
loads, for specified members. 

13. Automa tic Time Step Reductions : This feature permits the 
program to reduce the time step by multiple of halves in the event of a 
dynamic analysis failure. Number of time step reductions must be input 
by the user. 

14. Outpu t options : The program output options are available for 
joint displacements and reactions, member responses, and joint 
equilibrium errors. These options provide the opportunity for the user 
to suppress any unwanted results during static analysis. However, 
during dynamic analysis, these options are used to specifiy the time 
steps at which the results need to be printed. 

15. Joint Output: Joint displacements and reactions are printed at 
the end of each static load increment and at the requested time 
intervals for the dynamic analysis. Along with these results, shear 
panel internal moments are printed for rectangular frames that include 
joint shear deformations into the analysis. 

16. Member Output: Besides the member displacements and forces at 
the member stations (connections of discrete elements), strains (axial 
and curvatures at both hinges for flexural model; axial, shear, and 
curvature at the hinge for shear model) are listed against the 
respective forces along the directions of the deformed geometry, at the 
hinges of the discrete elements. 



94 

17. MEMBER and PRINT options : MEMBER option gives the member 
results for monitor members at each stage of the iteration processes. 
PRINT option lists the upper triangular stiffness, and load matrices for 
all the members and joints respectively in the local and global 
coordinate systems, in addition to the details given by the MEMBER 
option. Since these options produce a large amount of output, users are 
advised to request these options only when indepth details are needed to 
locate the source of error for convergent difficulties. 

18. Hyster esis Record : Hysteresis records of monitor members and 
joints are listed at the end of each dynamic run. Program allows to 
specify a maximum of 20 monitor members and joints. Member hysteresis 
includes the forces and displacements along the directions of original 
geometry at the member ends, and strains and the respective generalized 
forces along the directions of deformed geometry at the hinges next to 
member ends. Joint hysteresis includes joint displacements and shear 
moments, and plots displaying the variation of these parameters with 
t i me . 

19. SAVE option: This requests the program to save member and 
joint hysteresis records in either direct access storage devices (disks) 
or magnetic tapes depending on the Job Control Statements. Member 
responses along directions of original geometry and undeformed geometry, 
and joint responses can be stored in three different storage devices. 
The stored output can be used to plot the results of the entire dynamic 
analysis of the structure. 

20. Displa cement Controlled Analysis : Displacement of a node 
(joint) can be controlled by inputting a ^/ery large spring stiffness 
with a corresponding very large force at the joint, with magnitude of 






95 

the stiffness not exceeding 10 20 . A magnitude greater than 10 20 would 
cause excessive underflow that might interrupt the execution. 
21. General Comments : 

(a) FRAME82 and FRAME63 were both written for IBM 370. FRAME82 is 
compiled with Fortran H Extended Compiler with Optimization Level at 3, 
whereas FRAME63 was compiled with Fortran G Compiler. Note that Fortran 
H Extended Compiler with Optimization Level 3 produces a load module 
that requires half of the execution time needed for the load module 
obtained. by Fortran G Compiler to perform an analysis. The available 
FRAME63 program needs minor modifications to work on Fortran H Extented 
Compiler. 

(b) Subroutine FSUB1 of FRAME63 calls subroutines FSUB21 and 
FSUB22 the number of times equivalent to the order of the system of 
linear equations to be solved, to obtain stiffness and load matrices for 
joints and member respectively. In FRAME82, the above referred 
subroutines are modified so that FSUB21 and FSUB22 are called just once 
by FSUB1 for a system of equations. This modification made considerable 
saving (10-15%) in the computational time. FRAME82 uses a new 
subroutine FSUB23 to provide the stiffness and load matrices for joint 
solutions that include JSYES option. 

7.2 Program Structure 
The program consists of a number of "basic" subroutines which 
perform independent operations that are generally called by the main 
program numerous times. Basic subroutines are available to read and 
print the structure geometry data, member and joint stiffness and 
loading data; to trace inelastic behavior of the materials; to form 
discrete element stiffness matrices for flexural and shear models; to 






96 

form member stiffness and load matrices; to assemble the global 
stiffness and load matrices; to solve and print the member and joint 
responses, etc. Subroutine STATIC for static analysis, DYNA for dynamic 
analysis with no JSYES option and DYNAJS for dynamic analysis with JSYES 
option are the major subroutines in this program. STATIC calls several 
subroutines to carry out the static analysis of a frame. It also calls 
subroutines DYNA and DYNAJS after reading the structure data to perform 
dynamic analysis. Main program calls only subroutine STATIC to carry 
out the necessary operations and also has the COMMON statements for the 
variables defined in the COMMON blocks. 

The program employs four temporary and six permanent, direct access 
storage devices to perform a complete analysis of a structure. The 
temporary units store information of member stiffness and load matrices, 
and member supports during intermediate and final iterations. Three of 
the permanent files store the results pertaining to joints, joint 
supports and joint shear panels, and also the final results of all the 
member related information explained above. The program reads the last 
available good member and joint solutions including history dependent 
parameters from these permanent files during continuation runs. 
Hysteresis records of monitor members and joints are written in the 
other three permanent files. Appendix D gives descriptions and 
functions of these units with the space requirements. It also contains 
a list of job control statements required to execute FRAME82. 



CHAPTER 8 
VERIFICATIONS WITH ANALYTICAL SOLUTIONS 

8.0 Introduction 



This chapter is primarily intended to provide several example 
problems to test and verify the various features and options, such as 
Discrete Element Shear Model, joint shear, damping, etc., which are 
added to FRAME63 to develop FRAME82. The examples considered herein are 
either canti levered members or single story one bay frames, which have 
closed form mathematical solutions for most of the examples. The 
obtained results are compared with FRAME63 analysis and other available 
studies. 

Example 8.1 demonstrates how well the discrete element shear model 
predicts the response and the convergence rate with the number of 
elements in a member. The influence of shear on the buckling load and 
the post-buckling response of the column is illustrated in Example 
8.2. Example 8.3 shows how damping influences the structural 
response. The hysteresis behavior of the joint shear panel is 
investigated in Example 8.4 using a canti levered beam excited with a 
dynamic load. The influence of member shear and joint shear on a 
prismatic frame is studied in Example 8.5. All the features available 
in FRAME82 are utilized in the dynamic analysis of a frame subjected to 
1.5 El Centro earthquake in Example 8.6. 



97 



98 

8.1 Example of Deep Prismatic Canti levered Beam 
A three-foot long canti levered S12X31.8 steel beam is shown in 
Fig. 8.1 with its material and section properties (52). The beam is 
analyzed neglecting all large displacement effects (i.e. PDNO option on) 
and using a shear area factor of 1.0, for three different loading cases 
that are listed below. Also, linear elastic material response is 
assumed. 

Case 1: A 22 kips concentrated end load with uniform beam dead weight 

of 2.65 lbs/in. 
Case 2: 22 kips concentrated end load only. 
Case 3: A uniform load of 614 lbs/in. 

Both flexural and shear models are employed in the analysis. The beam 
is divided into 4, 8, 12, 16, and 20 elements in each loading case to 
study the convergence. The beam deflection at the free end is selected 
as a basis for comparison between analytical and closed form 
(theoretical) solutions. 

The theoretical solutions were obtained using the elementary 
structural analysis formulae, as follows. The flexural deflection due 
to concentrated end load and uniformly distributed load are given by 

Eqs. 8.1a and 8.1b: 
3 

5 f = 3ET (8.1a) 

. wL 4 

6 f = WT (8.1b) 

The shear deflection due to concentrated end load and uniformly 

distributed load are given by Eqs. 8.2a and 8.2b: 

kPL 

6 s = 7T5- (8.2a) 

s 

* _ i, r wx . k wL , 

S s " k J AT dx ; m ( 8 - 2b ) 

s s 



99 



f 



S12X31.8 

A36 STEEL 



3.0' 



0.35" — 



.5.0' 



o 



o 

o 



<\] 



I = 218 in^ 
A = 9.35 in 2 
\, = 3.82 in 2 
E = 29,000 ksi 
G = 11,200 ksi 
k = 1.0 



Figure 8.1 Canti levered Prismatic Deep Beam 















100 

The principle of superposition is used to obtain the deflection for the 
case of combined concentrated end load and uniform load. 

The solutions indicated in the tables as shear model and flexural 
type are obtained using the shear model but inputting a very high shear 
modulus such that the shear model would give the same results as the 
flexural model in the limit as the number of elements are increased. 
The results of each loading case are tabulated with theoretical 
solutions in Tables 8.1, 8.2, and 8.3 respectively. 

Shear deformations account for approximately 25 percent of total 
deflection in Cases 1 and 2, and 30 percent in Case 3. It is to be 
noted that a deep beam (depth span ratio - 1/3) is chosen in this 
example to yield large shear deformations. It is seen from Tables 8.1 
and 8.2 that the flexural model with n elements generally gives the same 
result as flexural type solution of the shear model with 2n elements. 
This is due to the fact that the flexural model has two flexural 
springs; whereas the shear model has one. However, in the case of 
uniformly distributed load, even four elements of the shear model 
predict the exact closed form value. It can easily be proven that a 
single shear model element will give the exact displacement for a beam 
under uniformly distributed load. Incidentally, it is noticed that the 
analytical results are equal to or lower than the theoretical values for 
all the cases other than flexural model case of the uniformly 
distributed load. The latter produces displacements larger than the 
exact value, i.e., it predicts upper bound displacement solution for 
uniformly distributed loading, while the other cases yield lower bound 
displacement solutions. 



Table 8.1 Concentrated End Load with Self Weight 



101 









Displacements (X 0.01 


in. ) 




I Model 


Type 


Number of Elements 


Theor. 
Solution 




4 


8 | 12 , 16 - 


20 


Shear 


Total 


7.191 


7.255 | 7.267 , 1 .111 . 


7.273 


7.276 | 




Flex. 


5.336 


5.400 | 5.411 | 5.415 . 


5.417 


5.421 | 


Flex. 


Total | 


5.400 


5.416 | 5.418 , 5.419 , 


5.420 , 


5.421 | 



Table 8.2 Concentrated End Load Only 



Model 






Di 


splacements (X 0.01 


in. ) 




Type 






Number of 


Elements 




Theor. 


4 


8 


1 lZ 


16 | 


20 


Solution 


Shear 


Total | 


7.179 


7.242 


1 7.254 


7.258 | 


7.260 


7.263 , 




Flex. 1 


5.327 


5.391 


■ 5.403 , 


5.407 | 


5.409 


5.412 , 


Flex. 


Total | 


5.391 


5.407 


1 5.410 . 


5.411 | 


5.411 , 


5.412 | 



Table 8.3 Uniformly Distributed Load 



1 






Di 


splacement 
Number of 


s (X 0.01 


in. ) 




Model 


Type 






Elements 




Theor. 
Solution 


4 


8 


1 12 1 


16 , 


20 


Shear 


Total 


2.969 


2.969 


I 2.969 | 


2.969 , 


2.969 


2.969 | 


Flex. 


2.039 


2.039 


I 2.039 , 


2.039 | 


2.039 


2.039 | 


Flex. 


Total | 


2.071 


2.047 


■ 2.043 | 


2.041 , 


2.040 | 


2.039 , 






102 

The computer solutions indicate close agreement with the 
theoretical values and the convergence is extremely good. The study 
indicates that 20-element shear model analysis is very close to 
convergence in all cases. 

8.2 Example on Buckling of a Prismatic Canti levered Beam 

To investigate the influence of shear deformations on buckling 
load, a vertical prismatic cantilevered beam shown in Fig. 8.2 with its 
elastic properties is considered. In view of Equations 2.20 and 2.21, 
the Euler critical load P E is 

P = 1*1 = 181.7 kips 
t 41/ 

and the critical load P cr with shear deformations is 

kP- 
P cr = P E C 1 + 1H^ = °- 986P E = 17 9-2 kips 

Twenty elements are used in both shear and flexural model analyses 
that include geometric nonlinearity. A shear area factor of 1.0 is 
used. A small lateral load Q=0.001P E , is used in the analysis to 
disturb the column from an unstable equilibrium position. Three 
computer runs, two with shear model (true G and 10 5 times the actual G), 
and one with flexural model were made. As expected, flexural model and 
shear model with 10 5 times the G results coincide with each other. The 
nondimensional axial load P/P E versus lateral displacement A/L curves of 
the flexural and shear model analyses are plotted in Fig. 8.3 along with 
theoretical solutions. 

The theoretical solutions are obtained using the large displacement 
theory. Reference 53 gives the following relationships for a 
cantilevered beam considering only the flexural deformations: 



103 




I = 25.4 in 4 
A = 5.43 in 2 
\, = 1.13 in 2 
L = 100 in 
E = 29,000 ksi 
G = 11,200 ksi 



k = 1.0 



P. = 



* 2 EI 



4L 



2- ■ 181.7 kips 



Figure 8.2 Canti levered Prismatic Col 



umn 



o 

CM 



0.00 



f 

/J 



3b* 
// 



•<" M 




0.20 Q. 40 

DEFLECTION 



A SHEAR MODEL 
+ FLEXURflL MODEL 
x FLEXURE-THEORETICAL 
% SHEAR-THEORETICAL 



o.so 



80 



Figure 8.3 Nondimensional Axial Load — Displacement Curve 



104 

3L = K ^P) (8.3a) 

3A = 2 P (8.3b) 



where 



6 = ^^ (8.4a) 



p ■ sin a 



7 (8.4b) 

in which a = the rotation of the free end from the original 

geometry, A = displacement of the free end, and K(p) = complete 

elliptic integral of the first kind. Note that the Euler load is given 
in Eq. 2.21 as 

p _ * 2 EI 



E ^T" (8.5) 



In view of Eqs. 8.3 through 8.5 

P_- 4K 2 (p) 

P F 2 (8.6a) 

A . 2p 

L ' F[pJ (8.6b) 

When flexural and shear deformations are taken into account, the 
following relationships can be obtained: 

3L = K <P> (8.7a) 

5A = 2 P (8.7b) 

where 

TTTi ^ f T j (8 - 8a ) 

s 

P = sin 7 (8.8b) 

Note that Eqs. 8.7a, 8.7b, and 8.8b are identical to Eqs. 8.3a, 8.3b, 
and 8.4b. The difference is only at the expression for 3, and this 
difference can be easily recognized when one looks at Eq. 2.19. 
Equations 8.7 and 8.8 give the required relationships as 



105 



P 4K*(p) 



1 

1 + 4K2 (P) . P E 
, 2 A S G 



(8.9a) 



A 
L 



kTpT 



(8.9b) 



The theoretical curves which are obtained from the above 
expressions using values of Elliptic Integrals tabulated in Ref. 7, 
coincide with the analytical curves for £ > 0.20. As expected, the 
shear model curve with true G yields more deflection than the flexural 
model curve for a given axial load. The effect of shear deformations on 
the solution is much less than in Example 8.1, since the depth span 
ratio of this example is about 1/20. 

8.3 Example on Mass Dependent Damping 

The canti levered beam shown in Fig. 8.4 is considered to study the 
influence of mass dependent damping on the elastic and inelastic 
responses of a structure. The system is assumed to be under static 
equilibrium when a dynamic load of 70 kips is suddenly applied at the 
free end. Neither P-A nor P-y moments are included in the analysis, in 
order to compare the numerical results with the theoretical values. The 
weight of the beam is neglected for simplicity. The shear model with 20 
elements is utilized in the analysis for all the following cases: 
(i) Elasto-Plastic Analysis with no damping. 

(II) Elasto-Plastic Analysis with 5% damping. 

(III) Elastic Analysis with no damping, 
(iv) Elastic Analysis with 5% damping. 

The natural period of this one-degree system including shear 
deformations, is 0.2348. A time increment of 0.02 seconds is adequate 
to obtain maximum deflection with good accuracy. However, a time 



106 



A 



A 



W14X142 



100' 



Suddenly Applied 
Vertical Load 



70 
kips 



15.50" 




(ksi). 



36.0-- 



0.0012 



0.012 e 



I = 1660.4 in 4 
A = 41.54 in 2 
A w = 8.58 in 2 
E = 30,000 ksi 
G = 11,500 ksi 



Figure 8.4 Cantilevered Beam Under Suddenly Applied End Load 



"1 


Q_ 


Q_ 


CL 


















T 


iX 


CL 


II 


L-l 


O 


L_J 


a 


F-! 


j«j 


F". 


^ 


1 


1 


1 


1 






107 


a 

CO 




o 








o 




a 

CD 




i—i 






CD 







C 
LU 

QJ 

CD 

u_ 

4- 
O 



+-> 

u 
0) 

4^ 

eu 



cxi 

CD 

i. 
3 



QIlQ31d3Q 



108 

increment of 0.01 seconds is used in the dynamic analysis, to avoid any 
significant phase shift, that would make direct comparison with 
theoretical solutions difficult. Theoretical solutions available in 
Ref. 4, for elastic analyses with damping and no damping match well the 
numerical results. 

The computer results plotted in Fig. 8.5 illustrate the importance 
of material inelasticity and damping. Material inelasticity yields more 
deflection but reduces the amplitude of vibration. Damping diminishes 
the amplitude of vibration with time and the system ultimately reaches 
the steady state response or equilibrium position. Also, an effect of 
material inelasticity is that the equilibrium position is shifted due to 
inelastic unloading. The elastic solutions is only valid if the 
material remains elastic and this particular example would require that 
the yield stress be 62.2 ksi., which is 72.8 percent greater than the 
specified yield stress. 

8.4 Example on Joint Shear Panel 

To verify that the analytical model correctly follows the inelastic 
loading and unloading paths, the cantiliver of Fig. 8.4 is again 
considered and the shear panel dimensions are given in Fig. 8.6 (a) 
along with the shear stress-strain curve of the joint. The connection 
is assumed to prevent any "horizontal" rotation, but permits "vertical" 
rotation and, thus, the bending moment at the cantilevered end is 
carried by the joint panel. None of the available references give the 
shear stress-strain curve for a connection of this nature. A post-yield 
stiffness of 15 percent is assumed up to four times the yield shear 
strain for the shear stress-strain curve. A dynamic analysis is 
performed with no mass and the dynamic load in Fig. 8.6 (b), at the free 






109 



n 



100' 



W14X142 





1.807 



7.228 



Y (X 0.001 rad) 



(a) Cantilever Beam with Connection Detail 
and Joint Shear Stress-Strain Curve 




0.4 Time 
(sec) 



(b) Dynamic Load 



Figure 8.6 Details for Joint Shear Panel Behavior Analysis 






110 



o 
I— 

C_3 



o 
in 

D -- 
I 



4 INELR3TIC 

+ LINEAR ELASTIC 

V RIGID 



* fe" 



\/ 

k y 

\ 

\ / 

\ / 



/ " 






/ \ 
/ ^V \ 



/A 



...%.. 



y 



0.00 0.10 0.20 

TIME (SEC) 



0.30 



0.40 



(a) Deflection of Free End with Time 




-0.08 -fl.OU 0.00 0.04 0.08 

PANEL DEFORMATION IRflD) CX10" 1 ) 
(b) Shear Panel Moment versus Distortion 



Figure 8.7 Cyclic Behavior of Joint Shear Panel and Cantilever Free End 






Ill 

end. Hence, the loading is essentially a gradually applied cyclic 
static load. The loading curve is chosen such that all points in the 
beam outside the joint remain elastic throughout the analysis. The beam 
is analyzed with prismatic properties, linear geometry option and 20 
elements. The following three cases are investigated: 
(i) Inelastic joint shear deformation 
(ii) Linearly elastic joint shear deformation 
(iii) Rigid Joint 

The deflection of the free end is plotted against time in Fig. 8.7 
(a) for all three cases and hysteretic behavior of the joint shear panel 
is plotted in Fig. 8.7 (b). The computer results are exactly the same 
as the theoretical solutions. For the case of rigid joint, theoretical 
solution is obtained using Eq. 8.1a. The deflection produced by joint 
shear panel deformation, assuming Masing inelasticity, is added to the 
deflection obtained from Eq. 8.1a to get the theoretical deflection for 
the other two cases. 

8.5 Example on Prismatic Frame Buckling 
The frame in Fig. 8.8 with prismatic section and elastic 
properties, and connection details, is selected from Ref. 1 to study the 
member and joint shear effects on the buckling load. The buckling load 
for this frame considering flexural stiffness and negligible joint size 
is 594.8 kips (8). Monotonically increasing equal vertical loads are 
applied at joints 2 and 3, while a constant lateral load of 0.595 kips 
is applied to joint 3 to avoid any convergence problems with large 
column axial loads. 

Joint shear deformations are considered at joints 2 and 3, and 
neglected at joints 1 and 4. The frame is analyzed with 12 and 20 






112 



en 



4.70' 



LO 



o 



p 

7 



lo 

CO 



X 

lo 



1 



W?\ 



S10X25.4 



179' 



LO 

CO 



X 

LO 



0.595' 



4 



i 



o 
o 



0.42" -* 



t = 
cw 

0.265" 




o 

LO 



SECTION 


I (in 4 ) 


A (in 2 ) 


Aw (in 2 ) 


W5X18.5 
S10X25.4 


25.4 
12.4 


5.43 
7.46 


1.13 
2.80 



E = 29,000 ksi 
G = 11,200 ksi 
k = 1.0 



Figure 8.8 Prismatic Frame Buckling Analysis Data 



113 

elements for columns and beams, respectively, and a shear area factor of 

1.0. The following four cases are studied: 

(i) Elastic joints with discrete element shear model for members, 
(i.e., shear deformations considered in member and joint region) 

(ii) Rigid joints with discrete element shear model for members, 
(i.e., no deformations within joint region) 

(111) Point joints with discrete elements shear model for members. 

(1v) Point joints with discrete element flexural model. 

The term Point joint refers to a joint that has negligible 
dimensions located at the intersection of the member centroidal axes. 
The vertical load increment is 40 kips up to 400 kips, 20 kips up to 520 
kips, and 10 kips until the solution diverges. 

The applied axial load is plotted against the horizontal deflection 
of joint 3, for all cases in Fig. 8.9. The analysis using Point joints 
with shear model exhibits a significantly lower buckling load than that 
of the flexural model analysis due to member shear deformations. 
Increased joint stiffness in the rigid joint with shear model analysis 
yields more resistant to buckling. However, the curves of Elastic and 
Point joints with shear model analyses almost coincide with each 
other. This could be explained as follows. Finite joint dimensions 
reduce the member lengths in the Elastic joint analysis. Even though 
joint shear deformations are included, axial and bending deformations 
are neglected over the joint shear panel. In the case of Point joints, 
members are longer and axial and bending deformations are included over 
the entire length; but, joint shear deformations are ignored. In the 
example problem, the joint shear deformations are almost equal to the 
additional axial and flexural deformations that is accounted for over 



THEORETICAL BUCKLING LORD 




* w 



it M 



—A 



114 




ji ELASTIC JOINT - SHEAR MODEL 
+ RIGID JOINT - SHEAR MODEL 
■ x POINT JOINT - SHEAR MODEL 
^ POINT JOINT - FLEXURflL MODEL 



era 



00 



1.00 



00 



1.00 



DEFLECTION (IN) 



Figure 8.9 Axial Load versus Roof Displacement Curve 



115 

the shear panel length in the Point joint analysis. While it is clear 
that the use of a joint shear model is more rational than extending the 
flexural deformations arbitrarily into the joint region, it is good that 
models that do not consider the joint shear deformations may not be too 
much in error, if the joint regions are considered as part of the 
flexural members. 

8.6 Single Sto ry Frame Subjected to 1.5 El Centro Earthquake 
A single story frame, analyzed by Latona (36) is selected to 
illustrate the application of FRAME82 to general inelastic analysis of a 
structure subjected to earthquake input. The frame and connection 
dimensions, gravity loads, section properties, and member stress-strain 
and joint shear stress-strain curves are given in Fig. 8.10. The post- 
yield stiffness parameter, recommended by Fielding and Chen (15), for 
corner joints is utilized to derive the joint shear stress-strain curve 
for the joints. Joint shear deformations are permitted only at the roof 
joints. The base of the columns are assumed to have Point joints with no 
shear deformations. The digital data of El Centro Earthquake available 
from Kanaan and Powell (30) are used as the input motion. 

Latona (36) and Santhanam (47) used the weight of the girder and 
upper halves of the columns, to obtain the equivalent lumped mass at the 
roof joints. The heavy concentrated gravity loads acting at girder ends 
are not considered towards the contribution of the masses in this 
analysis in order to make comparison with the available results. 
Controlled acceleration method is used to simulate the ground 
acceleration of the earthquake. The desired acceleration input is 
achieved by employing a huge mass of 10 20 at the base of each column, 
and premultiplying the input acceleration curve by the same factor 



116 



191' 



191* 



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m = 0.065 k.sec /in 

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CNJ 



77*77 



(20 El em.) 
(a) Frame Dimensions and Loads 



t. Number of 
I Sublayers 



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10.35' 



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O 



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dim (in) 


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(d) Section Properties 




0.012 



0.05 



(e) Member Stress-Strain 
Curve 




0.001807 



0.075 Y 



(f) Joint Shear Stress- 
Strain Curve 



Figure 8.10 Details for the Analysis of Latona's F 



rame 



117 

20 
10 . A time step of 0.02 seconds is found good enough to represent the 

earthquake input. The columns and beam are divided into 12 and 20 
discrete elements; flanges and web in each element are divided into two 
and four sublayers, respectively. 

The lateral displacement of the joint 2 relative to the base is 
plotted against time in Fig 8.11 for both shear and flexural model 
analyses. The flexural model analysis is exactly the same as of 
Santhanam's FRAME63 analysis. Shear model analysis yields more 
displacement than the flexural model analysis. However, the difference 
is not very significant in this particular example. This is due to 
joint shear panels being in the elastic region throughout the analysis, 
and the members being long compared to their depths. The shear moment 
versus panel distortion of joint 2 is plotted in Fig. 8.12. Since the 
shear panel yield moment is greater than the yield moments of the 
members, the shear panels at joints 2 and 3 remain in the elastic 
region. Figure 8.13 shows the time history of shear moment and moment 
at joint 2 for shear and flexural model analyses, respectively. The 
shear model analysis gives a slightly higher moment than the flexural 
model analysis. The rotations of fibers parallel to the global X and Y 
axes, in the joint shear panel 2 are plotted in Fig. 8.14 against the 
time. Since no joint effect is considered in the flexural model 
analysis, X and Y rotations are identical. It is interesting to observe 
that Y-rotation in the shear model analysis is very close to the 
rotation obtained in the flexural model anaysis. However, the X- 
rotation is much larger than the Y-rotation in the shear model 
analysis. Santhanam (47) has done an extensive comparison between 
FRAME63, CL0SE11 analyses and Latona's analysis. Figure 8.15 is 



113 



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Figure 8.12 Shear Panel Moment — Distortion Diagram for Joint 2 



120 





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123 

extracted from Ref. 47 to focus on the differences between each 
analysis. 

Latona (36) divides the member into a number of control sections, 
and each control section into an assemblage of fibers to monitor stress 
and strain at each layer. The member stiffness matrix is obtained by 
integrating over each cross-section to obtain the flexibility 
coefficients, integrating over the length of the member to obtain the 
member flexibility matrix, and inverting the flexibility matrix. An 
ideal elasto-plastic stress-strain relationship is assumed for each 
fiber. The behavior of the structure between time increments is assumed 
to be linear; the incremental displacement is computed using stiffness 
matrices at current and preceeding time steps. Geometry of the 
structure is updated by adding the displacements that occurred during 
the preceding increment to the joint coordinates at the beginning of 
each increment. Thus, P-A moment is included and P-y moment is 
ignored. Correction for equilibrium error at the end of each time 
increment is neglected. Neither member shear nor joint shear is 
included in his analysis. 

Santhanam's FRAME63 analysis is very similar to FRAME82 analysis, 
except it does not include member and joint shear deformations. The 
program CL0SE11 predicts the response of a closed coupled multiple 
degree freedom nonlinear elastic system using constant average 
acceleration method. This example was treated as a one degree of 
freedom in the CL0SE11 analysis. The nonlinear resistance-deformation 
input was obtained from the results of a series of static load analysis 
of the frame, using FRAME63. 



124 

It can be observed from Fig. 8.15 that the CL0SE11, FRAME63, and 
Latona's analyses give almost identical results up to 2.3 seconds. No 
significant deviation could be observed in this region due to the 
relatively small deformations. However, FRAME63 predicts much larger 
deformations and drift after 2.3 seconds. CL0SE11, FRAME63, and FRAME82 
analyses are based on the same numerical integration scheme. The non- 
drifting nature of the results of CLUSE11 in the later periods of time 
indicate that the drift in the results of FRAME63 is primarily due to 
material and geometric nonlinearities. In view of these formulations, 
it can be concluded that the omission of P-y moments in Latona's 
analysis is the major factor that contributes to the deviation between 
FRAME63 and Latona's analyses. 

Latona's dynamic analysis assumes lateral displacement of all 
joints at a given story level are identical and includes only lateral 
mode of vibration, i.e., rigid floor assumption is used. However, 
FRAME82 and FRAME63 analyses include both translational modes and 
neglect the inertia mass corresponding to rotational freedom. Figure 
8.15 illustrates also the importance of including the heavy concentrated 
loads at joints 2 and 3 into joint masses. 



CHAPTER 9 
COMPARISONS WITH AVAILABLE EXPERIMENTAL DATA 

9.0 Introduction 
Two examples with experimental results available are presented in 
this chapter to compare with the FRAME82 analysis. All the experimental 
investigations were carried out in the Structural Engineering Laboratory 
of the University of California, Berkeley. Inelastic behavior of a 
beam-column subassemblage (33) is investigated in Example 9.1. The 
behavior of the joint shear panel is focused in this example. The 
dynamic analysis of the three story single bay frame reported in Ref. 12 
is considered in Example 9.2. The structure is excited with a motion 
which is very similar to the El Centro Earthquake motion. The 
excitation was produced on the University of California, Berkeley, 
shaking table while attempting to simulate El Centro Earthquake. 
Digitized acceleration data from the University of California, Berkeley, 
were not available. Thus, the earthquake input graphs of Ref. 12 were 
digitized and used in the analysis. 

9.1 Example of Beam-Column Subassemblage 
Bertero et al . (3) and KRAWINKLER et al . (33) carried out 
experimental investigation of the simplest structural assemblage, a 
column with two beams framing into it, to study the interaction between 
the basic structural elements (beams, columns, and connections) under 
repeated loading, when combined into subassemblages within a frame. Two 
types of subassemblages, one representing an upper story and the other a 

125 



126 

lower story, were used to obtain a wide range of behavior that could be 
expected in subassemblages of high rise unbraced frames. Subassemblage 
A which represents a typical "upper story" has the following 
characteristics: Column is subjected to low axial load, while the beam 
end moment is primarily due to gravity loads, since the effect of the 
design lateral load is small. The flange and web of the column are thin 
and in general, horizontal stiffeners are required in the connection to 
prevent web crippling and column flange distortion. Subassemblage B 
which represents a typical "lower story" has the following properties: 
The column is subjected to high axial load and the contribution of 
gravity loads to the beam end moment is small compared to that of the 
lateral loads which generally govern the design. The flanges and web of 
the column are thick enough so that no horizontal stiffener is likely to 
be required in the connection, even though it is common practice to use 
one. In their experiment, horizontal stiffeners were used only for 
subassemblage A. 

"Specimen Bl" which is of the subassemblage B type is selected in 
the present analysis to compare with the FRAME82 results. The details 
of the test specimen Bl are given in Fig. 9.1. The beam ends 1 and 3 
are supported by rollers, upper column end 5 is hinged and lower column 
end 4 is free. The structure is subjected to concentrated gravity loads 
of magnitude 59.15 kips at the middle third points of the beams, a 
constant vertical load of 339.2 kips at joint 4 and a cyclic horizontal 
load H at joint 4. The FRAME82 analysis includes the self-weight of the 
beams. The measured dimensions and material properties of the test 
specimen are used in the analysis. 



127 



160" 



160' 



H 



53.33" | 53.33" , 53.33" , 53.33" , 53.33" , 53.33" 



QJ 



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CO 



59.15 k 59.15 k 

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59.15 k 59.15 k 

J 1 



V4 



(12 Elem.) 



1339.; 



(12 Elem.) 



o 



o 



(a) Idealized Subassemblage 



r-. 
ro 



8.191" 




(b) Connection Dimensions 



Number of 
Sublayers 

2 



t -4 
w 



.A. 



W 



(c) Cross-Secti 



on 



Member 


b (in) 


t f (in) 


d w (in) 


t w (in) 


w (k/in) 


Column 
Beam 


8.16 
5.04 


0.909 
0.328 


7.282 
13.044 


0.627 
0.239 


0.0056 
0.0018 



(d) Section Properties 



128 



a 
U 



y 



(e) Member cr-e Curve 




2.36 9.44 
(f) Joint t-y Curve 



52.97 Y 
(X 0.001) 





COLUMN 


W8X67 


BEAM 


W14X22 


web 


flange 


web 


flange 


s (X 10~ 3 ) 


1.58 


1.43 


1.54 


1.28 


e sh (X 10" 3 ) 
% (X 10" 3 ) 


7.0 


7.0 


23.0 


23.0 


30.8 


36.4 


37.6 


49.9 


a y (ksi) 


47.0 


42.5 


46.5 


38.5 


a sh ( ksi ) 


47.0 


42.5 


46.5 


38.5 


\ (ksi) 


66.0 


66.0 


56.0 


56.0 


E (ks1) 


29,800 


29,800 


30,100 


30,100 


E ch (ksi) 


800 


800 


650 


650 


G (ksi) 


11,460 


11,580 



(g) Material Properties 




3 Number of 
Cycles 



-3.51 



(h) Loading Program 
Figure 9.1 Details for Analysis of Beam-Column Subassemblage 



129 



The horizontal displacement of joint 4 is controlled during the 
analysis as in the case of the experiment. Figure 9.1 (h) shows the 
displacement controlled loading used in the analysis. In the 
experiment, each cycle shown in Fig. 9.1 (h) was repeated four times and 
it was observed that elastic unloading stiffness decreased with 
increasing column displacement. The present FRAME82 analysis does not 
include the stiffness degradation effects. Hence, one cycle is 
considered in the anallysis for every four cycles of the experiment to 
keep the computer cost low. 

The joint shear stress-strain curve is derived as explained in 
Chapter 5. The t-y curve, Fig. 9.1 (f), is obtained by adding the 
contribution of column flanges to post yield shear stress, predicted by 
Krawinkler, to the theoretical shear stress-strain curve derived from 
the flexural stress-strain curve, Fig. 9.1 (e). However, the plateau in 
the shear stress-strain curve is neglected and the strain hardening 
region of the panel is obtained by linearly connecting the values of the 
stresses at the strains 4 Yy and v Masing model is used to include 
inelastic behavior of the material. The slowly applied static loading 
is simulated by a dynamic analysis with no mass at joint 4 to avoid 
unnecessary output and to reduce cpu time. 

The horizontal load H versus the horizontal displacement S of joint 
4, and H versus the rotation 6 p of joint 2 are respectively plotted in 
Figures 9.2 and 9.3. One could observe that the analytical curves 
envelop the experimental curves in these diagrams. The deviation 
between the analytical and experimental curves is significant only in 
the region where load reversal occurs. This could be due to the usage 
of one load cycle in the analysis for four cycles that were used in the 



130 



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Figure 9.2 Horizontal Load H — Horizontal Displacement $ Di 



agram 



131 



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Figure 9.3 Horizontal Load H — Joint Rotation e Di 



agram 



o 



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MOMENT DIFFERENCE CURVE 



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PANEL DISTORTION CRRD) CXIO" 1 ) 



0. 12 



Figure 9.4 Joint Shear Moment — Joint Panel Distortion Diagram 



133 



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EXFERIMENTRL 



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PANEL DISTORTION (RRD) CX10" 1 ) 



0.12 



Figure 9.5 Difference of Beam End Moments — Joint Panel Distortion Di- 



agram 



134 



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CURVRTURE (RRD/IN) [X10~ 2 J 
(b) 



Figure 9.6 Moment — Curvature Diagrams at the Hinges closer to Joint 2 



135 



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A ANALYTICAL 
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-0.30 -0.20 -0.10 -0.00 

CURVATURE (RfiD/INJ CX10" 2 3 
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Figure 9.7 Beam End Moment — Curvature Diagrams at Joint 2 



136 



experiment for a chosen displacement range -and also the inability of 
Masing model to predict the degradation behavior of structures 
accurately (21, 47, 48). 

Joint shear panel moment is plotted against joint shear distortion 
in Fig. 9.4. Since no experimental joint shear moment data are 
available, difference of beam end moments at joint 2 is plotted instead 
of the joint shear moment for the experimental curve. Thus, a 
significant difference is noticed between the analytical and 
experimental curves of Fig. 9.4. The difference of beam end moments at 
joint 2 versus joint shear panel distortions is shown in Fig. 9.5. i t 
shows good agreement between experimental and analytical results. 

The bending moment and curvature of the beams at the discrete 
element hinges which are closer to joint 2 (6.5 inches away from the 
respective beam ends) are plotted in Fig. 9.6. However, th 
experimental curves correspond to beam end moments and the average 
curvatures over a beam length of 11 inches. Figure 9.7 gives the bea 
end moments versus the curvatures plots. The curvatures are defined as 
stated for the previous figure. 

9.2 Example of a Three Story Frame 
Clough and Tang (12, 13), and Tang and Clough (51) performed 
several dynamic tests on a three story steel frame to study the seismic 
behavior of a large-scale steel structure. The test structure shown in 
Fig. 9.8 (a) was excited on the 20 foot square earthquake simulator of 
the Earthquake Engineering Research Center, University of California, 
Berkeley. Two phases of tests were carried out to observe significant 
inelastic deformations in the structure. In the Phase I study, the 
joint panel zones of the structure were deliberately made understrength 



e 



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+ 



4.968" 



(a) Idealized 3 Story Frame and Typical Connection Detail 



PN, 



t -A 

w 



t f Number of 
! Sublayers 



d 4 

w 



Dim (in) 


Column 


Beam 


b 


5.0 


4.016 


tf 


0.367 


0.284 


d w 


4.234 


5.463 


*w 


0.246 


0.243 



(b) Cross-Section 



(c) Section Properties 



138 



a 
c 



y 




y E sh £ u 
(d) Member a-e Curve 



2.19 13.14 Y (X 0.001) 
(e) Joint t-y Curve 





COLUMN W5X16 


BEAM W6X12 


web 


flange 


web 


flange 


• e y (X 10" 3 ) 

£ sh (X 10 " 3 ) 
% (X 10" 3 ) 

a y (ksi) 

a sh ( ksi ) 
a u (ksi) 

E (ksi) 

E sh (ksi) 

G (ksi) 


1.46 
27.0 
70.5 
44.1 
44.1 
65.0 

30,300 
480 

11,650 


1.34 
19.7 
59.1 
39.8 
39.8 
65.4 

29,800 
650 

11,460 


1.61 
24.5 
61.2 
49.6 
49.6 
67.6 

30,900 
490 

11,880 


1.27 
15.2 
48.4 
39.2 
39.2 
63.6 

30,800 
735 

11,850 



(f) Material Properties 



Point Load (kips) 
Distributed Load (k/in) 
Mass (k.sec 2 /in) 



Damping 



1st FLOOR 



2.015 
0.00441 
0.006011X2 



2nd FLOOR 



2.025 
0.00426 
0.006009X2 



0.147% 



3rd FLOOR 



2.06 
0.00380 
0.006017X2 



(g) Load, Mass, and Damping 



Figure 9.8 Details for Analysis of 3 Story Frame 



139 



so that yielding was initiatied in these regions. In the Phase II 
study, the panel zones were strengthened with doubler plates, so that 
yielding occurred exclusively at column and beam ends. Several 
earthquake inputs are used in both Phase I and II structures. 

The experimental results obtained for the test designated as 
EC400-I are compared with FRAME82 analysis in this study. Figure 9.8 
shows the details of input of the test frame for the FRAME82 analysis. 
The bases of the frame are assumed to be rigid. Joint shear 
deformations are considered in the other joints. The members are 
discretized into finite number of elements as shown in Fig. 9.8 (a). 
Measured section and material properties are used in the analysis. The 
strain hardening stiffness of the joint shear stress-strain curve is 
taken as 0.17 times the modulus of rigidity, the experimentally observed 
value. Masing model option is used to incorporate material inelastic 
behavior. The tributary weight of the structural components is assumed 
as a uniformly distributed load over the girders. For the dynamic 
analysis, tributary mass of structural components and concentrated loads 
are lumped at the nodes. Joint masses are included in the equations of 
motion for structure along X and Y directions and rotational inertia is 
ignored. 

The graphical accelerogram of EC400-I, available in Ref. 12, is 
magnified by 380 percent in both acceleration and time axes directions, 
and then digitized using a Summagraphics TD48 electronic digitizer. 
Constant average acceleration method is employed to integrate the 
accelerogram to get velocity and displacement. The obtained 
acceleration data, and the velocities and displacements of the shaking 
table obtained by integration are plotted in Fig. 9.9 against time. 



140 




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142 

Digitized values need to be corrected to obtain the best possible 
integrated velocity and acceleration results. This is achieved by 
introducing corrections to the base line, such as to minimize the mean- 
squared table velocity (40). A seventh order base line correction curve 
is used in this example. 

Mass proportional damping (6=0) corresponding to the forced 
vibration test results of 0.147 percent critical for the first mode of 
the structure is specified. The obtained frequency of the structure 
2.273 cps for the first mode is used to calculate a: 

c = am = ?c =■ 2£/km 

I 
i.e. - - 2C(i) 2 . 25. - 2(0.147)2.273(2.) . .042 

A time step of 0.012 seconds, approximately half the time interval of 
digitization for recorded data is used. This time interval is adequate 
to insure numerical stability since the period of vibration for the 
first mode had been estimated as 0.44 seconds. 

The results obtained in the FRAME82 analysis e^re presented herein 
along with the available experimental observations. Since the 
analytical results reported by Tang and Clough were matched with the 
experimental values by varying several parameters, such as damping, 
their analytical results are not reproduced. Figure 9.10 displays 
accelerations, velocities and displacements of the shaking table 
obtained respectively for base line corrected accelerograms. The 
observed shaking table displacement is plotted in Fig. 9.10 (c) and 
follows a pattern ^/ery similar to ' the analytical curve. Relative 
displacements of each story with repsect to table and absolute table 
displacement are shown in Fig. 9.11. Figure 9.12 displays story drifts 
against time. The experimental curves are advanced by 0.1 seconds in 



143 



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149 

the relative story displacement and story drift plots in order to match 
the first peak with the analytical results. The analytical distortions 
of the joint shear panels along the right column are plotted in Fig. 
9.13 against time. The measured first floor joint shear panel 
distortion is also given in Fig. 9.13 (c). Figure 9.14 consists of the 
predicted hysteretic behavior of the joint shear panels along the right 
column. The respective experimental curves are not reproduced from Ref. 
12 as it is difficult to digitize these complicated plots. Experimental 
curves display a smooth transition from elastic to inelastic region 
instead of the abrupt change exhibited in Fig. 9.14. However, they are 
generally in good agreement with the DRAIN 2D results. Figure 9.15 
displays comparative plot of measured and predicted results for story 
shears. The analytical moments at the upper ends of the columns and 
girder ends for the first floor are plotted in Fig. 9.16. The measured 
moments are also plotted in Figs. 9.16 (c) and (d). 

The analytical plots given in Ref. 13 and 51 were obtained using 
the program DRAIN 2D that was developed by Kanaan and Powell (30). 
DRAIN 2D considers three degrees of freedom, namely, horizontal, 
vertical, and rotational displacements. Provision is made for degrees 
of freedom to be deleted or combined (for zero and identical 
displacements at different nodes) to obtain substantial reduction in the 
computer time. The structure is assumed to be composed of the following 
elements; namely, (i ) truss, (ii) beam-column, (iii) shear panel, and 
(iv) semi-rigid connection. All elements are assumed to have bilinear 
relationship between force and displacement. The interaction between 
axial force and moment may be specified in the beam-column element which 
is permitted to yield through the formation of concentrated plastic 



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Figure 9.14 Joint Shear Panel Moment— Time Di 



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158 

hinges at it ends. Additional nodes can be specified along a member so 
that spread of yielding can be studied. Inelastic axial deformations 
are assumed not to occur in beam-column elements, because of the 
difficulty of considering the interaction between axial and flexural 
deformations after yield in their finite element model. The P-A moment 
effect is taken into account by including a geometric stiffness based on 
the axial force under static loads. The influence of P-y moment and 
member shear deformations on the structural response are ignored. 
Static loads may be applied prior to the dynamic loading, but no 
yielding is permitted under these loads. The dynamic response is 
determined by step-by-step integration with a constant acceleration 
assumption within any step. The tangent stiffness method is employed to 
get the inelastic response of a structure. The program assumes a linear 
structural behavior within each time step. If the stiffness of the 
structure changes due to yielding or unloading within a time step, the 
stiffness matrix is recomputed at the end of that time step and the new 
stiffness matrix is used in the succeeding time step. Any unbalance in 
equilibrium resulting from a change in stiffness within a time step is 
eliminated by applying corrective loads in the subsequent time step. 
Diagonal mass matrix is utilized in the analysis. Viscous damping of 
mass-dependent and/or stiffness-dependent type may be specified. 

Clough and Tang (13), and Tang and Clough (51) used the idealized 
structural Model C shown in Fig. 9.17 in their DRAIN 2D analysis. The 
frame was discretized as an assemblage of nine beam-column, six shear 
panel and two semi-rigid connection elements. The semi-rigid 
connections were at the column ends. Rocking mechanism of the shaking 
table supported by vertical actuators that could reduce the overall 



159 



SYM. ABT. <l 




NODE (DiMENSIONLESS) 
CZ3 RIGID MEMBER END 

T$r ROLLER 
A HINGE 



Figure 9.17 Shaking Table Structure Interaction Model Used by Clouqh 
and Tang (13) 






160 



stiffness of the structure, was modeled with two vertical springs. The 
table was restrained from vertical translation by a hinge at its 
center. The actual dimensions of the members, post-yield strain 
hardening ratio of 17 percent for the panel zones, a rotational 
stiffness of 750,000 kip-in/rad for each semi-rigid connection, a time 
step of 0.01204 seconds and mass dependent damping of 1.5 percent 
critical for the first mode were input. The stiffness of the vertical 
springs was varied to match the first mode frequency of the model with 
the experimental observation. The tributary mass of structural 
components and static loads was assumed to be lumped at the nodes for 
the motions in the X direction only. A parabolic base line correction 
was applied to the table acceleration records in order to obtain the 
best possible integrated displacement results. 
Observations and Interpretations 

The following observations and interpretations are made about the 
FRAME82 analysis, DRAIN 2D analysis, and experimental results, 
(i) The FRAME82 analytical model yields a slightly higher period of 
vibration than the measured value. This, leads to phase shift 
which could be due to low damping, rigid base assumption, 
inadequate number of discrete elements per member, large time 
step, etc. It is to be pointed out that the pitching motion of 
the shaking table would have reduced the frequency of the 
structure. 

(11) The predicted and measured response amplitudes match at the first 
peak. However, the predicted response oscillates through a large 
amplitude, while the measured response damps out. The damping 
could be increased to obtain better amplitude and phase 






161 

correlations. The measured 0.147 percent critical damping for 
the first mode of the structure is used in this analysis. Tang 
used 1.5 percent critical damping, which is about ten times 
greater than the measured value in the program developed by 
Kanaan and Powell (30) to match the computed and mesured results 
in References 13 and 51. 
(iii) The dead load and load history effects were disregarded in the 
experimental results available in Ref. 12. EC400-I is one among 
the several test runs performed on the Phase I structure. 
However, the predicted results include dead load effect. Even 
though FRAME82 is capable of including load history effect the 
present example does not include stresses due to previous 
loadings since the load history is not listed completely in Ref. 
12. Moreover, the computer cost to include all prior load 
histories would be beyond the budget of this study. The plotted 
experimental curves for shear panel distortions and first floor 
column and girder moments are obtained by adding the analytical 
dead load effects to the experimental plots given in Ref. 12. 
(iv) The joint shear panel distortion-time diagrams in Fig. 9.13 
display permanent deformations which are not exhibited in either 
experimental or analytical curves given in References 12, 13, and 
51. Joint shear panel predicted hysteresis loops shown in Fig. 
9.14 and experimental hysteresis loops available in Ref. 12 show 
inelastic deformations at the joints. The structure that had 
been tested underwent several test runs prior to this particular 
run and it would have had residual deformations at the beginning 
of the test. This would reduce the permanent deformations for 



162 

this particular run. It can be observed from Fig. 9.14 (c) that 
the shear strain oscillates approximately between 2.5y and -4y 
for the first floor shear panel. If it would have oscillated 
within a range of 2y y , one could attempt to justify the absence 
of permanent deformations using shake-down principle. Permanent 
deformations need to be displayed at all the joints where the 
range of oscillation is greater than 2y unless the load is 
applied such that the net permanent deformations are zero. It 
seems unlikely that with these large inelastic excursions, the 
net permanent shear deformations would be zero in all the joint 
shear panels, as reported in the DRAIN 2D analysis. Even Kabe 
(28) pointed out that DRAIN 2D analysis predicted considerable 
error in the permanent deformations when a different three-story 
frame was tested at the University of California, Los Angeles. 
The permanent deformations are easily seen only on the joint 
response curves. It is hard to observe any permanent set in 
member response curves. This is primarily due to the fact that 
this example structure is intentionally designed understrength at 
joints to have large inelastic deformations at the joint shear 
panels and elastic behavior in the members. Since joint shear 
panels are the primary structural components that undergo 
inelastic deformations, the permanent deformations are pronounced 
in the joint shear panel plots, 
vi) Though DRAIN 2D analysis predicted good results for this example, 
it did not display any permanent deformations at the joint shear 
panels. The major factors that would have contributed to this 
discrepancy are discussed in this paragraph. The DRAIN 2D 



(v) 



163 



assumes linear structural behavior within each time step. It 
corrects any change in the stiffness of the structure and any 
unbalance in equilibrium as corrective load, in the subsequent 
time step. This error is rectified in the FRAME82 analysis by 
updating the stiffness after each iteration and adding the 
corrective load at the beginning of next iteration, within a time 
step. The ignoring of dead load and load history in the DRAIN 2D 
analysis would also have influenced the joint shear panel 
response to a considerable extent since shear panels are the 
primary components that are subjected to inelastic 
deformations. FRAME82 results reported in this study includes 
the dead load stresses. 
In conclusion, better results could be obtained by using a larger 
damping in the FRAME82 analysis. It would display residual deformations 
at the joint shear panels that were not obtained from the DRAIN 2D 
analysis. The rocking motion of the shaking table can easily be 
incorporated in the FRAME82 analysis by properly modifying the support 
conditions of the model. 



CHAPTER 10 
CONCLUSIONS AND RECOMMENDATIONS 



10.1 Conclusions 
The main objective of this research was to develop a computer aided 
analysis of the inelastic static and dynamic behavior of plane frame 
structures including member and joint shear deformations. A new 
Discrete Shear Element Model is developed to include member shear 
deformations along with flexural and axial deformations, and nonlinear 
geometry. An additional rotational degree of freedom is utilized for 
each joint to devise a technique to incorporate joint shear 
deformations. The theory and the developed program FRAME82 are 
presented in this report. Besides the shear deformations, FRAME82 
considers nonlinear geometry, inelastic material response, cyclic 
loading, inelastic member and joint supports, mass dependent viscous 
damping, etc. The program formulates the structure stiffness matrix 
from the stress-strain level of the component materials, and perform 
member and joint solutions separately using tangent stiffness method. 

The program is verified with several simple structures that have 
theoretical solutions. A pair of structures which were tested at the 
University of California at Berkeley are analyzed with FRAME82. The 
analytical results have shown generally good agreement with the 
experimental responses and the solutions given by other analyses. It is 
observed that FRAME82 analysis predicts residual deformations of joint 
shear panels, that were not exhibited in the DRAIN 2D analysis. 



164 



165 

10.2 Recommendations 

Even though FRAME82 employs efficient solution procedures, it 
requires more computer time than many other existing programs to analyze 
a structure. This is due to the fact that the program is highly complex 
since it formulates the structure stiffness from the stress-strain 
level. It is, however, very economical to use FRAME82 to analyze a 
structure, instead of carrying out an experimental investigation. 
FRAME82 inelastic analysis is recommended for moderate size plane frame 
structures which have a maximum of 25 joints and 50 members. 

With regard to the future of the program, the following 
improvements and features can be added into the program. 

1. The program is currently restricted to rectangular frames with 
no diagonal bracing when including joint shear deformations in the 
analysis. The program ' can be modified so as to include joint shear 
deformations in the analysis of any plane frame with/without diagonal 
bracing. 

2. The program assumes that the member shear stress does not 
exceed the yield shear stress and takes only the linear shear 
deformations into account. A general shear stress-strain curve can be 
incorporated into the program to include inelastic member shear 
deformations without much difficulty. 

3. Interaction between axial and flexural stresses is considered 
in the member stiffness formulation. No interaction is considered 
between shear, and the axial and flexural stresses. Any one of the 
strain hardening assumptions such as isotropic hardening, kinematic 
hardening, etc., can be utilized to include the interaction between 
axial, flexural, and shear stresses. 



166 

4. In the case of joints, only the shear deformations are 
considered in the analysis. More experimental and theoretical 
investigations are needed to include axial and flexural deformations 
into the joint shear model. 

5. Stiffness dependent viscous damping can be incorporated into 
the program which presently considers only the mass dependent viscous 
damping. Stiffness dependent damping plays an important role on the 
response of the structure at higher modes of vibration. 

6. Discrete shear element model can be used only for linear 
elastic, nonlinear elastic, and masing inelastic stress-strain curves. 
The new model can be extended to include masing inelasticity with 
stiffness degradation and special mild steel model type behavior for the 
member flexural stress-strain curves. 

7. Computation of structure stiffness from the stress-strain 
curves of each member layer facilitates identifying the correct positi 
of plastic hinges, and incorporating the partial plastification of th 
sections into the analysis. This method requires a lot of bookkeeping 
operations and more computer time, which makes the FRAME82 analysis yery 
expensive. Instead of performing the analysis at the stress-strain 
level, the analysis can be made considering the overall behavior of the 
cross-sections, which is commonly found in literature, at the expense of 
some accuracy to reduce the computer cost. A comparison can be made 
between the results obtained by different types of analyses. 

8. Lateral and torsional buckling of members and buckling of joint 
shear panels can be included in the analysis. 

9. The program performs inelastic unloading only for structural 
components which are prescribed to have symmetric stress-strain 



on 

e 



167 



curves. The possibility of including a more general stress-strain curve 
can be studied. 

10. Input formats can be extended to include automatic generation 
of stress-strain curves and cross section data for standard steel 
sections. This modification would make the program more convenient to 
the user for design analysis. 

11. FRAME82 is written for the analysis of plane frame 
structures. This can be extended to perform inelastic analysis for 
three-dimensional frames without losing the important features available 
in this program. While a three-dimensional static nonlinear elastic 
program has been written by Mitchell (38), the development of a three- 
dimensional dynamic, inelastic analysis program with the generality of 
FRAME82 would require considerable work. 



APPENDIX A 
DISCRETE SHEAR ELEMENT MATRICES 

This appendix contains the matrices involved in the formulation of 
stiffness matrix 'for the discrete element shear model discussed in 
Chapter 3. The required matrices for the stiffness matrix of discrete 
element flexural model are available in References 22 and 47. 

The discrete element deformations $ a> fi m , and 5 gJ and the angle 6, 
defined in Eqs. 3.1 through 3.4 are rewritten in Eqs. A.l through A. 4: 

6 a = (2h+oj 4 -aj 1 ) sec 6 - h cos (wj-e) - h cos (ug-8) (A.l) 
6 m = "e"^ (A. 2) 

6 s = h sin (c V 6 ) + h sin K" 8) ( A " 3 ) 



-1 f V^g , 
n ^h+^-tu^ (A. 4) 



In order to simplify the presentation the following parameters 
H, tp and i|> 2 are defined in Eqs. A. 5 through A. 7. 

H = 2h+w 4 -(D 1 (A>5) 

*1 = V 9 (A. 6) 

*2=V 9 (A. 7) 

A.l Initial Stress Stiffness Matrices 

In view of Eqs. 3.37 and 3.41, the elements of the initial stress 

stiffness matrices associated with axial force and shear force, kST- • 

and kSV-j j , can respectively be written as in Eqs. A. 8 and A. 9: 



168 



169 



9 2 6 



kST. . 



kSV. . 
1J 



= T 



3fcj. 3<u. 
1 J 



2 

3^6 



3ou. 3oj. 

i J 



(A. 8) 



(A. 9) 



The above equations imply that [k] ST and [k] sv are symmetrical square 
matrices of order 6. Since the computation involves extensive algebra, 
only the final results are presented herein. 

The initial stiffness matrix associated with axial force, [k] ST is 
given in Eq. A. 10: 



[k] 



ST 



kst 



11 



kst ]_2 


kst 13 


-kstn 


-kst 12 


kst 22 


kst 23 


-kst 12 


-kst 22 




kst 33 


-kst 13 


-kst 23 






kst n 


kst 12 

kst22 



L 



symmetric 



kst 16 


kst 26 





-kst 16 


-kst 26 


kst 66 



(A. 10) 



in which 



kst ll = 7 sin6 sin29 - 5 sin28 cos 2 9 

+ j sin 26 (cos^ + cos^ 2 ) 

kst 12 = -H sine cos 2 9 + 6 cos2e cos 2 e 
h _,_„„ . 2 



kst 



kst 



13 



16 



7jrSin2e cos 9 (cos<K + cosily) 

Hh ■ Q Q 

— 2 sin29 cosiK 
Hh 



~T 



sin29 cos^, 



kst 



3 



22 = H cos 9 + 5 s sin29 cos 9 + h cos efcosik+cos^. 



kst 23 « Hh cos 9 cosiK 
kst 26 = Hh cos 2 9 cosif> 2 



(A. 10a) 

(A. 10b) 
(A. 10c) 
(A.lOd) 
(A.lOe) 
(A.lOf) 
(A.10g) 









170 



kst 33 = Hi costp 1 
kst g6 = HI cos^ 2 



(A.lOh) 
(A.lOi) 



The initial stiffness matrix associated with shear force, [k] is 
presented in Eq. A. 11: 



[k] 



sv-^F 



ksv 



11 



ksv 



12 



ksv 



22 



_ 



symmetric 



ksv 



13 



ksv 



ksv 



23 



33 



•ksv 



-ksv 



11 



12 



-ksv 



ksv 



13 



11 



■ksv 



12 



-ksv 



22 



-ksv 



23 



ksv 



12 



ksv 



22 



ksv 



ksv 



16 



26 




-ksv 16 



-ksv 



ksv 



26 



66 



(a.ii; 



in which 



ksv 



ksv 



ksv 



11 



12 



= -h sine cos 6 (cos^+cosip-) — | sin 28 

2 ^ ? 

■ h cos29 cos 6 (cos^+cos^) + -4 sin20 cos 6 

Hh 



13 = — 2 sin26 simp. 



ksv 



16 



ksv 



22 



JSj- sin29 s i n ^ 2 
2 



h sin26 cos 9 (cos^+cos^ ) - 5 cos 9 



ksvpo = -Hh cos 9 si nip 



23 



1 



ksv 



26 



- Hh cos 9 simp. 



ksv 33 = - H h simp 

2 
ksv 6 g = -H h simp 2 



1 



(A. 11a) 
(A. lib) 
(A. lie) 
(A. lid) 
(A. lie) 
(A.llf) 
(A.llg) 
(A.llh) 
(A. Hi) 



171 



A. 2 Incremental Deformation-Displacement Matrix [B] 
An element of the matrix [B] is given in Eq. 3.8 as 



where 



and 



Thus 



9e. 

d = i_ 

ij 3 W . 



a m s 



M - [Wp 0J 2 , 0J 3 , 0J 4 , 0J 5 , OJg] 



[B] 



T\ 



b ll b 12 b 13 " b ll -bi2 b 16 
-H o H 

b 31 b 32 b 33 " b 31 " b 32 b 36 



in which 



b n = -H cose - _| sin29 

b 12 = -H sine + 6 cos 2 e 

b^ = Hh si nip-, 

b 16 = ^ h si n^2 

b 31 = " Y sin2e (cos^ 1 + cos^ 2 ; 

b 32 = h cos e (cosily + cos* 2 ) 

b 33 ~ ^ cos ^-\ 
b 36 = Hh C0S ^9 



(A. 12) 



(A. 13) 



(A. 14; 



(A. 15) 



(A. 15a) 
(A. 15b) 
(A. 15c) 
(A.15d) 
(A.15e) 
(A.15f) 
(A.15g) 
(A.15h) 



A. 3 Incremental Force-Deformation Matrix [D] 
The equations (4.38, 4.41, 4.43, 4.45, 4.46) derived in Chapter 4 
are summarized underneath to obtain the incremental force-deformation 
matrix [D]: 






172 



[D] = 



217 



3T_ 

9£ c 

3M 
3e 



9T 
3<j) 



T-r 



3M 
3cf> 



ii 



in which 



3T_ 

3e 



m A. "■ 



= E 



E E. 



c j-1 "j 1=1 ' 



3T 3M 



3<f> 3e 



m A. n j 
- E -A. E 



3_V 
3Y 



y-E- 



3M J A j "j 2 

aX * 2 -*L E yf E. 

9<f> j-l n j 1=1 * 1 1 



3V '" 

4e = E C . A. G. 



9y 



j = l 



SJ J J 



(A. 16) 



(A. 16a) 



(A. 16b) 



(A. 16c) 



(A.16d) 



For the special case of a linear elastic material of modulus of 
elasticity E and modulus of rigidity G, assuming average cross-sectional 
area A, shear area A s , and second moment of area I, the matrix [D] 
becomes 

AE 

EI 



[D] = 



2h~ 







U A S G 



(A. 17) 



A. 4 Discrete Shear Element Matrices and Other Essential 
Relationships Excluding Geometric Nonl inearities 

The matrices presented in sections A.l and A. 2 include the effects 

of geometric nonlinearity described in Chapter 3, and the matrices in 

section A. 3 include the material nonlinearity described in Chapter 4. 

Sometimes, it may be needed to analyze structures considering material 

nonlinearity and neglecting geometric nonlinearity. Hence, the matrices 



173 

given in sections A.l and A. 2, and the deformation-displacement 
relationships and equlibrium equations given in Chapter 3 are presented 
beow ignoring geometric nonlinearities. 

[k] ST = [Null] (A>18) 

[k] sv - [Null] (A#19) 



[B] = 



-10 10 
0-1001 
1 h -1 h 



J 



(A. 20) 



Deformation -Displacement Relationships 



K " W ?) 



2h 
6 m = w 6 " w 3 



fi = h(oj + oj ) + (oj _ u ) 



(A. 21a) 
(A. 21b) 
(A. 21c) 
(A.21d) 



Equilibrium Equations 



f l 


= 


-T 




f 2 


= 


V 




f 3 


= 


-M 


+ Vh 


f 4 


= 


T 




f 5 


= 


-V 




f 6 


- 


M + 


Vh 



(A. 22a) 
(A. 22b) 
(A. 22c) 
(A.22d) 
(A.22e) 
(A.22f) 



APPENDIX B 
CONSTANT AVERAGE ACCELERATION METHOD 

The acceleration {w} is assumed to be constant between adjacent 
time stations. Therefore, the acceleration between stations j and j+1 
is given by 

{w}=|{w. + w j+1 } (Bil) 

The velocity {w} at any time within the same interval can be obtained by 

{w} = {w} + / {W}dt 

J t. 
J 



i-e. {W} = {%}. +\ (t-tj) (\l + W. +1 } 



Hence, the velocity at station j+1 is 



(B.2) 



(w} j+1 ={w} j+ f {w j+ w. +1 } (B . 3) 

where At = time increment 

The displacement at station j+1 is given by 

{w} j+l = {w} j + 1 ! ^} dt 

i.e. {W} j+1 ■ {W}. + At{W.} +4"^J + VlJ (B.4) 

Equations B.3 and B.4 are the basis for constant average acceleration 

174 



175 

method of numerical integration. The incremental velocity {aW}, and 

incremental acceleration {aw}, can be obtained as a function of 

incremental displacement JAW} at time station j, and time increment At, 
from Equations B.3 and B.4 and are given by 

{A*}. =- 2 { W }. ^{AW}. (B . 5) 

{AW}. = -2{W}. -4_{W}. +-^{AW}j (B.6) 



APPENDIX C 
INPUT GUIDE FOR FRAME82 

Units of force, distance, and time must be consistent throughout the 
input data. 3 

Dimensions of the input variables are given within brackets. 
Input data corresponding to the fourth degree of freedom' (v) will be 
disregarded in the analysis if the option (JSYES) to include joint shear 
deformations is not exercised. 



IDENTIFICATION OF RUN 
(Two statements per run) 

Stat Col Format Entry 

1 1-80 10A8 Description to identify the run. 
1-80 10A8 Continuation of the description. 

IDENTIFICATION OF PROBLEM 
(One statement per problem) 
The program stops if the Problem Number is CEASE . 

Entry 
Problem Number. 

PDNO to exclude geometric nonl inearity, 
JSYES to incorporate joint shear 
deformations. 

Description of the Problem. 
See Note 1 



Enter M8ER for output of member iteration details. 

Enter RINT for stiffness matrices output. 

Enter SAVE to save member and joint hysteresis on storage devices. 

TABLE 1 - PROGRAM CONTROL DATA 
(Three statements per problem) 

Hold options are specified for Tables 2-7 in the first statement. The 
program holds data only if data were input in the preceeding problem. 
Hold option is not applicable for problem types 1 and 9. 

Second statement contains output options for Tables 8, 9, and 10. 

176 



Stat 


Col 


Format 


1 


1-5 


A5 




6-9 


A4 




11-15 


A5 




16-76 


A5, 7A8 




77-80 


A4 


Note 1 










1 1-5 


15 


6-10 


15 


11-15 


15 


16-20 


15 


21-25 


15 


26-30 


15 


31-35 


15 


36-40 


15 


41-45 


15 


46-50 


15 


51-55 


15 


56-60 


15 


61-65 


15 


66-70 


15 


71-75 


15 



177 

Number of statements in Tables 2-7 are specified in the third statement. 

Stat Col Format Entry 

Problem Type (see Note 2) 
1 to Hold Prior Data for Table 2. 
1 to Hold Prior Data for Table 3A. 
1 to Hold Prior Data for Table 3B. 
1 to Hold Prior Data for Table 3C. 
1 to Hold Prior Data for Table 4A. 
1 to Hold Prior Data for Table 4B. 
1 to Hold Prior Data for Table 4C. 
1 to Hold Prior Data for Table 4D. 
1 to Hold Prior Data for Table 4E. 
1 to Hold Prior Data for Table 5A. 
1 to Hold Prior Data for Table 5B. 
1 to Hold Prior Data for Table 5C. 
1 to Hold Prior Data for Table 5D. 

1 to Hold Prior Data for Table 6. 

2 to Hold Prior Data for Table 6 and then 
to Modify by a certain % to be specified 
in Table 6. 

76-80 I5 1 to Hold Prior Data for Table 7. 

Note 2 

Available problem types are listed below: 

1 - A new problem (always static) - Results not held from precedinq 

problem. 

2 - Static problem - Results held from preceding satic problem 

3 - Dynamic problem - Results held from preceding static problem 

4 - Dynamic problem - Results held from preceding dynamic problem. 

9 - Read for structure data only - Does not affect the results of the 
preceding problem available on disk from prior run. 

Stat Col Format Entry 

15 1 to suppress output Table 8 in Static 

analysis. £r_ 

Increments "of time steps after which Table 

8 is t0 b e printed during Dynamic analysis. 
b-iU I5 1 to suppress output Table 9 in Static 

analysis. _or_ 

Increments of time steps after which Table 
.. ._ Tc 9 is to be printed during Dynamic analysis. 

li_ib ib 1 to suppress output Table 10 in Static 

analysis, or 

Increments of time steps after which Table 

10 is to be printed during Dynamic 

analysis. 

Stat Col Format Entry 

Number of Statements in Table 2. 

Number of Statements in Table 3A. 

Number of Statements in Table 3B. 

Number of Statements in Table 3C. 



3 


6-10 


15 




11-15 


15 




16-20 


15 




21-25 


15 



178 



26-30 I5 Number of Statements in Table 4A. 

31-35 I5 Number of Statements in Table 4B. 

36-40 I5 Number of Statements in Table 4C. 

41-45 I5 Number of Statements in Table 4D. 

46-50 I5 Number of Statements in Table 4E. 

51-55 I5 Number of Statements in Table 5A. 

56-60 I5 Number of Statements in Table 5B. 

61-65 I5 Number of Statements in Table 5C. 

66-70 I5 Number of Statements in Table 5D. 

71-75 I5 Number of Statements in Table 6. 

76-80 I5 Number of Statements in Table 7. 



TABLE 2 - FRAME GEOMETRY DATA 
(Number of statements as per Table 1) 

Stat Col Format Entry 

1 11-15 I 5 Number of Joints. 

21-25 15 Reference Joint. 

31-40 E10.3 X-Coordinate of the reference joint [d]. 

41-50 E10.3 Y-Coordinate of the reference joint [d]. 

61-70 E10.3 Joint Location Tolerance [d]. 

2nd and succeeding statements prescribe the x and y offsets of the TO 
joints with respect to the FROM joint. 

Stat Col Format Entry 

2/2+11-15 ~T5 From JWF. 

21-30 E10.3 X-Offset [d]. 

31-40 E10.3 Y-Offset [d]. 

46- 80 715 TO Joints (see Note 3). 

Note 3 

Several joints can be specified in one statement if offsets between any 
two adjacent TO joints are equal to the offset between the FROM joint 
and the first TO joint 



TABLE 3A - JOINT DATA 
(Number ot statements as per Table 1) 

Stat Col Format Entry 

1 1-5 I5 Number of Joint Stiffness Types. 

2nd and su cceeding statements specify the joint stiffness type for each 
joint. 

Stat Col Format Entry 

2/2+ 1-5 15 Joint Stiffness Type. 
11-80 1415 Joint Numbers. 

3rd and successive statements give the dimensions and shear stress- 
strain curve for each joint stiffness type. 



179 




h. h 

» — ».— ______ 



Stat Col Format Entry 

Joint Stiffness Type. 

h. [d]. 

hp [d]. 

v b [d]. 

v t [d]. 

Thickness of the panel [dl. 

Modulus of Rigidity* [f/d 2 ].. 

Shear Stress-Strain Curve Number*. 

Either modulus of rigidity or curve number can be specified. 



3/3+ 


1-5 


15 




11-15 


E10.3 




21-30 


E10.3 




31-40 


E10.3 




41-50 


E10.3 




51-60 


E10.3 




61-70 


E10.3 




71-75 


15 



TABLE 3B - JOINT SHEAR STRESS-STRAIN CURVES 
( Number of statements as per Table 1: Two per cu rve ) 



The program is currently 
Hence, leave the columns 
degradation factors blank. 

Stat Col Format 
1 



restricted to 
corresponding 



Masing inelastic 
to material and 



behavior, 
stiffness 



Entry 
Material ("Enter MILD if the special model 
for mild steel is to be used. Otherwise, 
leave it blank). 
Curve Number. 
Number of Points. 
Symmetry Option (see Note 4). 
Stiffness Degradation a Factor. 
Stiffness Degradation 3 Factor. 
Shear Stress - Values. 

Entry 
Shear Stress Multiplier [f/d 2 ]. 
Shear Strain Multiplier [d/d]. 
Shear - Strain Values. 

Note 4 

If equal to 1 a symmetrical branch is provided internally. The first 
stress and strain values must be zero if the symmetry option is used. 
The curve must be symmetric to perform inelastic analysis. 



Stat 



2-5 


A4 


6-10 


15 


11-15 


15 


16-20 


15 


21-30 


E10.3 


31-40 


E10.3 


41-80 


815 


Col 


Format 


1-10 


E10.3 


11-20 


E10.3 


41-80 


815 



180 



TABLE 3C - MEMBER LOCATION DATA 
(NumDer ot statements as per Table 1) 

Stat Col Format Entry 

1 11-15 I5 Number of Member Stiffness Types. 

21-25 I5 Number of Member Load Types. 

2nd and succeeding statements prescribe stiffness and load types for 
every member. yy 

Stat Col Format Entry 

2 / 2+ 6-10 15 FROM JoW. 

16 " 2 15 Stiffness Type. 

2 1" 2 5 15 Load Type. " 



31-80 1015 TO Joints (see Note 5). 

Note 5 

tho b ppnM Wlt , h *. ame + %V ffneSS and 1oad types as of the member - connecting 
the FROM and first TO joints, can be specified if the FROM joint of each 
new member is the TO joint of the previous one. 

TABLE 4A - INCREMENTAL JOINT LOADS AND SUPPORT LINEAR 

RESTRAINTS IN STRUCTURE x, y, and z AXES 

(Number of joints as per Table 1: Two statements per joint) 

Stat Col Format Entry 

Joint: 

Load Parallel to x-Axis [f]. 
Load Parallel to y-Axis [f]. 
M z Moment [fd]. 
M v Moment [fd]. 



Stat 



1-5 


15 


11-20 


E10.3 


21-30 


E10.3 


31-40 


E10.3 


41-50 


E10.3 


Col 


Format 


11-20 


E10.3 


21-30 


E10.3 


31-40 


E10.3 


41-50 


E10.3 


71-80 


E10.3 



Entry 
Restraint Parallel to x-Axis [f/d]. 
Restraint Parallel to y-Axis [f/d]. 
R z Restraint [fd]. 
R v Restraint [fd]. 
Mass [f/g] (see Note 6). 



Note 6 

A negative input mass will cause mass to be omitted in equation of 
motion for structure y displacement and a positive mass to be used in 
equation of motion in structure x direction. A positive input mass 
makes the program to use mass in both x and y equations. 

TABLE 4B - NONLINEAR JOINT SUPPORTS 
(Number of statements as per Table 1) 

Stat Col Format Entry 

1 1-5 15 Joints 

11-20 E10.3 Q-Multiplier [f or fd]. 

21-30 E10.3 W-Mulitplier [f or fd]. 






41-45 
46-50 
51-55 
56-60 
61-65 
66-70 
76-80 



15 
15 
15 
15 
15 
15 
15 



181 



Curve Number of Force Restraint // to x- 
Axis . 

Curve Number of Force Restraint // to y- 
Axis. 

Curve Number of Moment Restraint about z 

Direction. 

Curve Number of Moment Restraint about v 

Di recti on. 

Curve Number of Force Restraint // to x'- 
Axis. 

Curve Number of Force Restraint //to y'- 

Axi s . 

Stiffness Type (see Note 7). 



Note 7 

If curves are specified along member directions, stiffness type of the 
member is required. 



TABLE 4C - NONLINEAR SUPPORT CURVES 
(Number of statements as per Table 1: Two per curve) 



Stat Col Format 



1 


6-10 


15 




11-15 


15 




16-20 


15 




26-80 


1115 


Stat 


Col 


Format 


2 


26-80 


1115 


Note 8 







Entry 
Curve Number. 
Number of Points. 
Symmetry Option (see Note 8) 
Q-Values. 

Entry 
W-Values. 



If equal to 1 

and W values 

case, Q-W will be inelastic of the Mas ing" type 



a symmetrical branch is provided internally, 
must be zero h' symmetry option is equal to 



The 



first Q 
In this 



TABLE 4D - DYNAMIC JOINT FORCES 
(Number of statements as per Table 1) 



Stat Col Format 



1 6-10 


15 


11-20 


E10.3 


21-30 


E10.3 


31-40 


E10.3 


41-50 


E10.3 


51-60 


E10.3 


61-65 


15 


66-70 


15 


71-75 


15 


76-80 


15 



Entry 
Joint Number. 
F x -Axis Multiplier [f]. 
Fy-Axis Multiplier [f]. 
Mj-Axis Multiplier [fd]. 
M y -Axis Multiplier [fd]. 
Time Axis Multiplier [t]. 
Curve Number // to x Axis. 
Curve Number // to y Axis. 
Curve Number // to z Direction 
Curve Number // to v Direction, 



. .. . 



Stat Col 


Format 


1 6-10 


15 


11-15 


15 


26-80 


1115 


1+ 1-80 


1615 



182 



TABLE 4E - DYNAMIC JOINT FORCE CURVES 
(Number of statements as per Table 1: nominally 2 statements per curve) 

Entry 
Curve Number. 
Number of Points. 
Force Values. 

Continue the remaining Force Values on the 
succeeding statements. 

Stat Col Format Entry 

2 2OT0 1115 TlmeTOes. 

2+ 1-80 1615 Continue the remaining Time Values on 

succeeding statements. 

TABLE 5A - MEMBER STIFFNESS TYPES 

(Number of statements as per Table 1: Number of sets of statements is 

equal to the number of stiffness types defined in this problem) 

Stat Col Format Entry 

1 l -5 15 Stiffness Type. 

6-10 I5 Number of Elements (see Note 9). 

11-20 E10.3 Modulus of Elasticity [f/d 2 ] (Blank if 

Nonlinear 0ption=l). 
21-25 A5 Element Type. 

SHEAR if member shear deformations are to 

be included. 

FLEX to neglect member shear deformation 

effects. 
31-40 E10.3 Prismatic Moment of Inertia [d 4 ] (Blank if 

specified below). 
41-50 E10.3 Prismatic Area [d 2 ] (Blank if specified 

below). 
51-55 15 Nonlinear Option. 

Blank to exclude material nonlinearity 

effects. 

1 to include material nonlinearity effects. 
56-60 I5 Number of Statements that Follow. 

61-65 15 Axis Option. 

1, if restraints are in the direction of 
member axes. 

2, if restraints are in the direction of 
structure axes. 

In both cases, restraints are per unit of 
length along the member x'-axis, and 
distances are along the member x'-axis. 
66-70 15 Output Option. 

If Blank, complete beam-column output is 

given. If 1, only member end forces are 

given. 

FROM Joint Option (see Note 10). 



71-75 15 



76-80 I5 TO Joint Option (see Note 11 



183 



Note 9 

Number of elements must be between 4 and 20. If Blank, 20 elements are 
used. If even number of elements are used, displacements and 
equilibrium errors are printed at the center station for monitor 
member. If odd number of elements are used, they are printed at the 
first station from the center towards the FROM joint. 



Note 10 



If 1, the member is assumed pinned to joint at FROM end. If Blank the 
member is assumed rigidly connected to joint at FROM end. If -ij,' the 
member is assumed to be rigidly connected to the joint at FROM end and 
to have 1 rigid discrete elements followed by j discrete elements that 
remain linear regardless of stress level. 



Note 11 

If 1, the member is assumed pinned to joint at TO end. If Blank, the 
member is assumed rigidly connected to joint at TO end. If -ij the 
member is assumed to be rigidly connected to the joint at TO end and to 
have i rigid discrete elements followed by j discrete elements that 
remain linear regardless of stress level. 

2nd statement is required only for Prismatic Memb ers with Element Type = 
SHEAR and Nonlinear Option Blank. " -" 

Stat Col Format Entry 

T~ TTTO tlU.3 Modulus of Rigidity [f/d 2 ]. 

11-20 E10.3 Effective Shear Area [d 2 ]. 

3rd and succeeding statements of the set if Nonlinear Opti on is Blank 
and Element Type = FLEX . An example presented at the end of this 
appendix illustrates the input of this particular statement. 

Stat Col Format Entry 

3/3+ 11-20 E10.3 From TDTIFance) [d]. 

21-30 E10.3 To (Distance) [d]. 

31-40 E10.3 Moment of Inertia (I) [d 4 ] 

41-50 E10.3 Flexural Area (A) [d 2 ]. 

51-60 E10.3 Restraint // to x' or x Axis (S x .) [f/d 2 ] 

61-70 E10.3 Restraint // to y' or y Axis (Sji) [f/d 2 ]. 

71-80 E10.3 Rotational Restraint about z -Axis (S i] 

[f]. z 

3rd and succeeding statements of the set if Nonlinear Option = 1 . 

Stat Col Format Entry 

3/3+ 11-15 15 Cross Section # at FROM Joint. 

15-20 I5 q-w Curve # at FROM Joint // to x' or x 

Axis . 

21-25 I5 q-w Curve # at FROM Joint // to y' or y 

Axis. 

26-30 I5 q-w Curve # at FROM Joint about z' Axis. 

36-40 I5 Cross Section # at TO Joint. 

41-45 15 q-w Curve # at TO Joint // to x' or x Axis. 

46-50 I5 q-w Curve # at TO Joint // to y 1 or y Axis. 






184 



51-55 


15 


61-70 


E10.3 


71-80 


E10.3 



q-w Curve # at TO Joint about 
q-Multiplier [f/d or f], 
w-Multiplier [d or d/d]. 



Axis. 



TABLE 5B - CROSS-SECTION PROPERTIES 
(Number of statements as per lable 1: Number of sets of statements 
equal to the number of cross-sections defined in this problem ) 



TS 



1st statement of the set, 
Stat Col Format 



1 



6- 

11- 



10 
15 



15 

15 



Entry 
Cross-Section Number, 
Number of Statements 



that Follow, 



2nd and succeeding statements of the set. 



Stat Col Format 

2/2+ 6-10 "75 

11-20 E10.3 

21-30 E10.3 

31-40 E10.3 

41-45 15 



Entry 
Number of Equal Layers (see Note 
Width or Outside Diameter [d]. 
Depth or Thickness [d]. 
Centroidal Distance [d]. 
Area Option. 

input is 
equal 



12). 



46-50 


15 


51-60 


E10.3 


61-70 


E10.3 


71-80 


E10.3 



If Blank, 

rectangle. 

properties of thin wall tube 

Curve Number. 

Stress-Multiplier [f/d 2 ]. 

Strain-Multiplier [d/d]. 

Shear Area Coefficient. 



properties 
to 1, input 



of 
is 



Note 12 

If Blank, cr-e will be nonlinear but 
symmetric for inelastic treatment, and 
in a cross section must be < 10. 



elastic. If 
the sum total 



not, a-e must be 
of all the layers 



TABLE 5C - MEMBER STRESS-STRAIN CURVES 
(Number of statements as per lable 1: Two per curve if flexural model 
is employed and Three per curve if shear model is employed.) 



Stat Col Format 



1 


2-5 


A4 




6-10 


15 




11-15 


15 




16-20 


15 




21-30 


E10.3 




31-40 


E10.3 




41-80 


815 


Stat 


Col 


Format 



41-80 815 



Entry 
Material (Enter MILD if the special model 
for mild steel is to be used. Otherwise 
leave it Blank). 
Curve Number. 

Number of Points (see Note 13). 
Symmetry Option (see Note 14). 
Stiffness Degradation a Factor. 
Stiffness Degradation 3 Factor. 
Flexural Stress - Values. 



Entry 
Flexural Strain 



Values. 



185 



Note 13 

must "be 1 * 4° f ° ll0W inelaStic path ' number of P oints including origin 

Note 14 

If equal to 1, a symmetrical branch is provided internally. The first 
stress and strain values must be zero if the symmetry option is used 
The curve must be symmetric to perform inelastic analysis. 

mnli 5 ^™^ iS , : ec l u :: ed for the set only ^ discrete element shea r 
model is employed for this particular cross -sect i b~h~. ~ — 

Stat Col Format Entry 

3 1-10 E10.3 Elastic Shear Modulus [f/d 2 ]. 

TABLE 5D - NONLINEAR MEMBER SUPPORT CUR VES 
(Number of statements as per Table 1: Iwo per curve ) 

Stat Col Format Entry 

Curve Number. 

Number of Points. 

Symmetry Option (see Note 15). 

q-Values. 

Entry 
w-Values. 

Note 15 

If equal to 1, a symmetrical branch is provided internally. The first a 
and w values must be zero if the symmetry option is used. Then q-w 
will be inelastic of the Masing type. M 

TABLE 6 - MEMBER LOAD DATA 

(Number of statements as per Table 1: Number of sets of statements 

equal to the number of load types defined in this problem) 

Member loads may be input by any one of the four axis options outlined 

Q a is the concentrated load in the direction of the a-axis 

q a b is the distributed load in the direction of the a-axi's and has its 

intensity per unit of length along the b-axis. 

Concentrated loads may not be input at distance of 0.0. 



1 6-10 


15 


11-15 


15 


16-20 


15 


26-80 


1115 


Stat Col 


Format 


2 26-80 


1115 



186 



1st statement of the set 
Stat Col Format 



1 



6-10 
11-20 

21-25 
31-40 



15 
E10.3 

A5 
E10.3 



41-50 E10.3 



56-60 


15 


61-65 


15 


80 


Al 



AXIS OPTION 1 




From" Joint 



Entry 
Load Type. 
% Increase in Load. 
Blank Unless Hold Option = 
DITTO (see Note 16). 
Uniform Load // to x 1 Axis 
Blank, if second statement 
Uniform Load // to y' Axis 
Blank, if second statement 
Number of Statements that 
1 (Axis Option). 
* (see Note 17). 



2. 



(q x v) L" f / d l- 

is used. 

(q y »y ' ) 
is used 



[f/d]. 



Fol 



ow, 



Note 16 

inJ n Y y °1 DITT0 " ni cause a11 the load types higher than the current 

HdJt,^ 6 ! hT 9 1* flnSd t0 h3Ve the Same % increase wi thout providing 
additional data statements for them. y 

Note 17 



^hif 7A*K? Ve 7 n ' d f any % 0f load incr ease or reduction specified in 
Table 6 or Table 7 and maintains constant member load. 



2nd and succeeding statements of the set, 



Stat Col Format 
2/2+ 11-20 

21-30 

31-40 



41-50 

51-60 

80 



E10.3 
E10.3 
E10.3 

E10.3 

E10.3 

Al 



Entry 
From Distance x 
To Distance 
Load // to 
Q x ' or q 
Load 



.along member) [d], 
x' (along member) [d]. 
('-Axis. 
V L" f or f/d], 
V 

q y V ( f or f /d; 

about z'-Axis. 
Q z ; or q . i [fd or f], 
* (see Note 17). 



Qy> or 
Moment 



// to y'-Axis 






187 



AXIS OPTION 2 




From Joint 



1st statement of the set. 



Stat Col Format 



1 



6-10 
11-20 

21-25 
31-40 



15 
E10.3 

A5 
E10.3 



41-50 E10.3 



56-60 

61-65 

80 



15 
15 
Al 



Entry 
Load Type. 
% Increase in Load. 
Blank Unless Hold Option = 2. 
DITTO (see Note 16). 
Uniform Load // to x-Axis (q xx <) [f/d] 
Blank, if second statement is used. 
Uniform Load // to y-Axis (q vy i) [f/d], 
Blank, if second statement il used. 
Number of Statements that Follow. 
2 (Axis Option). 
* (see Note 17). 



2nd and succeeding statements of the set 



Stat Col Format 
2/7+" 1T720 

21-30 

31-40 



41-50 

51-60 

80 



E10.3 
E10.3 
E10.3 

E10.3 

E10.3 

Al 



Entry 
From Distance x' (along member) [d], 
To Distance s' (along member) [d]. 
Load // to x'Axis. 
Q x or q xx r [f or f/d]. 
Load // to y'-Axis. 

' Cf or f/d]. 
out z'-Axis. 
or q z i x i [fd or f]. 
(see Note 17). 



Qy or q 
Moment 



2»' 



AXIS OPTION 3 



Distance x (Negative 
as shown here) 




188 



1st statement of the set. 



Stat Col 


Format 


1 6-10 


15 


11-20 


E10.3 


21-25 


A5 


31-40 


E10.3 



Entry 

Load Type. 

% Increase in Load. 

Blank Unless Hold Option = 2. 

DITTO (see Note 16). 

Uniform Load // to x-Axis (q ) [f/d]. 

Blank, if second statement i s used. 
41-50 E10.3 Uniform Load // to y-Axis (q ) [f/d]. 

Blank, if second statement is used. 
b6-6 ° I5 Number of Statements that Follow. 

61-65 15 3 (Axis Option). 

80 Al * (see Note 17). 

2nd and succeeding statements of the set. 

Stat Col Format Entry 

2/2+ ?!in cJS'o From Distance x (along structure axis) [d]. 

H'in rJS'X To Distance x (along structure axis) [d], 

31-40 E10.3 Load // to x-Axis. 

Q x or q [f or f/d]. 
41-50 E10.3 Load / /*{ y-Axis. 

Q x or q [f or f/d]. 
51-60 E10.3 Moment about z'-Axis. 

Q z i or q 7 i ■ [fd or f]. 
80 Al * z ( see Note 17). 

AXIS OPTION 4 
It is identical to Axis Option 3 except distances are in structure y- 
axis and 4 is input in column 65 of the first statement. 



The member x'-axis goes from the FROM joint to the TO joint. The I 

and 

illu; 

(22), 



and TO joints are determined by input of Table 3. An example 
' ;rating various axis options is given at the end of this appendix 



TABLE 7 - ITERATION CONTROL 
(Two statements unless held from previous problem) 

1st statement contains frame solution parameters. 

Stat Col Format Entry 

" 5 _ I5 # of Load Reductions. 

# of Time Step Halvings. 
Maximum Number of Iterations. 

# of Time Steps. 
Force Error [f]. 
Moment Error [fd]. 
Size of Time Step [t], 
% Reduction of Joint Load. 
Total Number of Monitor Joints (< 20 
Monitor Joint Numbers. 



1-5 


15 


6-10 


15 


11-15 


15 


16-20 


15 


21-30 


E10.3 


31-40 


E10.3 


41-50 


E10.3 


51-55 


F5.2 


56-60 


15 


61-80 


415 



coefficient. 




Stat 


Col 


Format 


2 


1-10 


E10.3 




11-15 


15 




16-20 


15 




21-30 


E10.3 




31-40 


E10.3 




51-55 


F5.2 




56-60 


15 




61-80 


415 


2+ 


1-80 


1615 


Note 18 







189 

+1 1-80 1615 Continue the remaining Monitor Joint 

Numbers on the succeeding statements. 

2nd statement contains member solution parameters and dampinq 

Entry 
Mass Dependent Damping Constant (a) [1/t]. 
Monitor Joint option (see Note 18). 
Maximum Number of Iterations. 
Force Error [f]. 
Moment Error [fd]. 
% Reduction of Member Load. 
Total Number of Monitor Members (< 20). 
Monitor Member Numbers. 

Continue the remaining Monitor Members on 
the succeeding statements. 

for output of actual displacements of monitor joints in time varyinq 
plots. J b 

1 for_ output of monitor joint displacements with respect to first 
monitor joint in time varying plots. 

2 for output of monitor joint displacements with respect to the 
previously input monitor joints in time varying plots (i.e. 1+1 with 
respect to i ). 



COMMENTS ON INPUT GUIDE 
General 

The data statements must be stacked in proper order for the program 
to run. 3 

The last statement of the data must contain CEASE in the first five 
columns to stop execution. 

A consistent system of units of force [f], distance [d], and time 
LtJ must be used for all input data - e.g., pounds, inches, and seconds. 

Input data correspond to fourth degree of freedom (v) will be 
disregarded in the analysis if JSYES (Joint Shear YES) option is not 

MBER (meMBER) and RINT (pRINT) options will assist you to detect 
any convergence problems. Remember that these options will produce huqe 
output. 3 

SAVE option saves member and joint hysteresis on storage devices. 

Majority of the five-space words are integers. 

All ten-space words are floating-point decimal numbers. 






190 

All numbers must be right justified. 

The Problem Number may contain alphanumeric characters. 

Table 1 - Program Control Data 

Data are accumulated in Tables 2 through 7 until the corresponding 
Hold Options are left blank in Table 1. 

The maximum number of statements that can be accumulated in Table 
5A is 50 plus the number of Stiffness Types. 

The maximum number of statements that can be accumulated in Table 
6A is 75 plus the number of Load Types. 

Type 1 problems start the iterative solution with zero 
displacements. 

Type 2, 3, and 4 problems use the displacements of the previous 
problem in their first iteration. 

Type 9 problem reads structure data only. 

Output Options for dynamic solutions require input of the time step 
increment between output. A zero or blank gives output only the final 
time step. A one gives output for every time step and generates a lot 
of output. 

Table 2 - Frame Geometry Data 

The first statement gives the total number of joints in the frame 
which must not exceed 25. 

The reference joint, its coordinates, and the joint location 
tolerance are given only if the Hold Option for Table 2 is not 
exercised. 

Joints are numbered from 1 to the total number of joints. A joint 
number may not be deleted in a series unless the Hold Option is not 
exercised. However, the joint may be structurally deleted by removing 
all members intersecitng at the joint. 

The reference joint may be any joint and it may have any 
coordinates, except that it and other joint coordinates must be less 
than 1.0E+20. 

The maximum difference in joint numbers, for joints that are 
connected by members is 5. 

The second and succeeding statements in Table 2 specify the 
location of all additional joints in the frame at least once. If Hold 
Option is used, only the new joints must be specified. 



191 



All offsets must be FROM a previously located joint TO another 
joint. The TO joint may be a previously defined joint. This allows the 
user to check the locations of the joints. If the error in the location 
of the joint is within the joint location tolerance, then the solution 
continues; otherwise, the solution terminates with an appropriate 
diagnostic. 

The joint location tolerance should allow for normal round-off 
error. If offsets are input to the nearest 0.1 inch, then a joint 
location tolerance of 0.3 inch will be usually sufficient for a 
moderate-sized frame. 

The repetition of the TO joint allows the user to locate up to 
seven joints with one statement, if the offsets between the adjacent new 
TO joints are the same as between the FROM joint and the first TO joint. 

It is not necessary for offsets to be given at locations where 
members are. However, the location of all joints must be specified at 
least once. 

Table 3A - Joint Data 



The joint data is required to incorporate the joint shear 
deformation effects into the analysis. Only the rectangular joint 
panels can be prescribed at present. 

The first statement gives the total number of Joint Stiffness Types 
in the frame, which must not exceed 25. 

In order for the joints to have same stiffness type, they must have 
the same dimensions and stress-strain properties. 

Joints with the same stiffness type can be specified in a single 
statement. However, a maximum of 14 joint numbers can be specified in 
any desired order in a single statement. 

Joint Stiffness Type of zero (0) may be input to include joints 
with negligible stiffness (dimensions). 

The properties of the Joint Stiffness Types can be input in any 
order. 

Either modulus of rigidity or joint shear stress-strain curve shall 
be specified. 

A maximum of eight different joint shear stress-strain curves can 
be specified. 



Table 3B - Joint Shear Stress-Strain Cur 



ve 



The joint shear stress-strain curves need not be input in the order 
of the curve numbers. 



192 



The t-y curves must be input such that the y values are in the 
ascending algebraic order. 

Usually shear stress and shear strain values will have the same 
sign. 

A maximum of eight points can be input for each curve. 

Ant i -symmetrical curves may be input by specifying only the 
positive displacement branch including the origin (0,0). 

Table 3C - Member Location Data 



The first ' statement gives the total number of member stiffness 
types and the total number of member load types. 

Member stiffness and load types (other than zero) are numbered from 
one to their total number. The total number of member stiffness and 
load types must not exceed 25 individually. 

The total number of members in the frame must not exceed 50. 

Type zero stiffness is used to delete a previously defined 
stiffness. Type zero load is used to indicate no load on the member. 
The restrictions on length, orientation etc. outlined below, do not 
apply to members with zero stiffness type and zero load type. 

In order for two members to have the same stiffness type, they must 
have the same length, the same angular orientation in the frame, and the 
same stiffness properties with respect to their FROM and TO joints. 

In order for two members to have the same load type, they must have 
the same length, the same angular orientation in the frame, and the same 
stiffness properties with respect to their FROM and TO joints. 

The member coordinate axes are defined by the FROM and TO joints 

specified. The member x'-axis starts at the FROM joint and goes to the 

TO joint. The member y'-axis and z'-axis are located from the member 
x -axis by the right hand rule. 

All members in the frame must be assigned a stiffness type and a 
load type. This assignment is not accumulative for a member in the 
frame; i.e., the last values of stiffness and load types specified 
replace the previous values. Thus, stiffness and load types of a member 
must be specified on the same statement. 

Up to ten members with the same stiffness and load types may be 
located with a single statement if the FROM joint of each new member is 
the TO joint of the previous one. 

Table 4A - Incremental Joint Loads and Support Linear Restraints 

All joint loads and linear supports (restraints) are specified with 
respect to the structure axes. 



193 

Joint loads and restraints are accumulated in Table 4A. 

M v moment and R y restraint will be included in the analysis only if 
JSYES option is exercised. 

Structure supports may be input as linear elastic joint restraints 
(springs). Complete fixity of a joint may be achieved by inputting a 
very large value for the spring stiffness. No round-off errors are 
encountered when extremely large values are specified unless larqe 
values are input and then subtracted away. 

Complete freedom of joint movements is obtained by not specifying 
any restraints at a joint. 

A displacement may be enforced by specifying a very large restraint 
and a corresponding force equal to the desired displacement times the 
large restraint. 

Table 4B - Nonlinear Joint Supports 

The latest curve numbers, including zero (which deletes any old 
curve number), replace the old curve numbers at a joint. Curves may 
have any number from 1 to 20. 

A joint may have both linear supports (Table 4A) and nonlinear 
supports (Table 4B) 

Curve number corresponding to moment restraint in the v-direction 
is considered only if JSYES option is specified. 

Curves may be specified in both structure and member directions. 
If curves are specified in member directions, then the stiffness type of 
the member which the curves are referenced to must be given. 

The Q and W multipliers input in Table 4B times the Q-W curves 
input in Table 4C yield the final Q-W values at a joint. 

The ratio of the final Q-values to the final W-values should not bp 
many orders of magnitude larger than the stiffness data for the members 
of the frame, if the supports are specified in member directions. 

Table 4C - Nonlinear Support Curves 

The Q-W curves do not have to be input in the ascending order of 
the curve numbers. 

The Q-W curves must be input such that the final W values will be 
in ascending algebraic order. 

Normal Q-W curves will have opposite signs for displacements and 
forces. 

Anti -symmetrical curves may be input by specifying only the 
positive displacement branch including the origin. 



194 




*Anti -Symmetrical Curve* 




Input Curve 



Table 4D - Dynamic Joint Forces 

Dynamic joint forces need not be input in the ascending order of 
the joint numbers. 

Joint load curve number shall not exceed 20. 

•« icvrc ve number ^responding to M moment is ignored in the analysis 
if JSYES option is not specified. 

TAble 4E - Dynamic Joint Force Curves 

The latest force-time values input to the dynamic joint force curve 
replace the previously assigned values. 

Curves can be input in any desired order. 

A maximum of 300 points can be input for a curve. 

Table 5A - Member Stiffness Types 

Stiffness type must be input in ascending order. If Table 5A is 
held from the previous problem, then the first new stiffness type in 
able 5A (if any) must be equal to the number of stiffness types in the 
last problem plus one. 

Discrete element flexural and shear models can be specified for 
prismatic members and members with material nonlinearity. But only 
flexural model can be specified for members with linearly varying 
stiffness properties. 

Prismatic members with FLEX (flexural) element type and a sinqle 

modulus of elasticity may be input with one statement, if no member 

restraint is present. Other members with FLEX element type require two 
or more statements. 

Prismatic members with SHEAR element type and a single modulus of 
elasticity may be input with two statements, if the member has no 
restraints. Other members with SHEAR element type require three or more 
statements. 

If more than one statement is used to describe a member stiffness 
type with FLEX element type, the prismatic stiffness properties must be 
left blank. 



195 

^u^ur^n 30 tW0 statemen ts are used to describe a member stiffness 
left blank "* tyPe ' ^ prismat1c stiff ness properties must be 

If the nonlinear option is left blank, then the third and 
succeeding statements describe the variation in the linear stiffness 
properties of the members. This type of input is illustrated later in 
this appendix. 

If any of the member stiffness properties are nonlinear, the 
nonlinear option is set equal to one and the third statement gives the 
cross section numbers, and q-w curve numbers, and q and w multipliers 
at the member FROM and TO joints. Then the cross section properties' 
stress-strain curves, and q-w curves are defined in Tables 5B, 5C, and 

The final q-w values used are the product of the q and w 
multipliers and the q-w curves input in Table 5D. 

roniJ^^ 1 ^^^ 11 ^! 1 ^ 3 ' cross sect1on numbers, and curve numbers 
replace the old data, if any, at a joint. 

Cross sections and q-w curves may have any number from 1 to 20. 

Effective shear area is equal to the shear carrying area divided by 
shear area factor. Note that shear area factor is very similar to the 
inverse of shear area coefficient used in Table 5B. 

Table 5B - Cross Section Properties 

Cross-sections do not have to be input in the order of their 
numbers. 

Cross sections are defined as a series of up to 10 peices Each 
pence may be either a rectangle or a thin wall tube and have a unique 
flexural stress-strain curve number up to 8. The final stress-strain 
values are the product of the stress and strain multipliers, and the 
stress-strain curves input in Table 5C. (Each piece may be subdivided 
into specified number of layers for inelastic treatment. The total 
number of sublayers for the whole cross section must be < 10.) 

The centroidal distance input for the tube and the rectangle is the 
distance from the member x'-axis to the centroid of the pipe or 
rectangle. This distance is positive if it is along the direction of 
the member y -axis. Linear interpolation along the length of the member 
between corresponding pieces is provided in the program. Thus the 
cross section input at the two end joints should have the same number of 
pieces and pieces should be input in the same order. Interpolation 
between a rectangular piece and a tubular piece is not allowed. 

All data input for a cross section number replaces the previous 
data, if any, for that cross-section number. 



196 

Shear area coefficient times the area of the piece is the 
contribution of the piece to the shear area of the cross-section. The 
summation of such areas gives the effective shear area for the cross- 

Table 5C - Member Stress-Strain Curves 

Member flexural stress-strain curves are input similar to the Q-W 
same Ve si g °n. 9b1e 4C " N ° rmally ' StreSS and stra1n values ^ have the 

Corresponding pieces in the cross-sections at the two end ioints 

curves 6 Th^ "iT ^ ° f P ° intS ° n their flexural stress-strain 
m JJll' rl • ^ .° WS lnear lnter Polation along the length of the 
member. If inelastic algorithm is specified, the corresponding pieces 
must have exactly the same a-e curve at the two ends of the member 

m nH Q i ElaSti V!' ear u m0duluS iS s P ecifl 'ed only if discrete element SHEAR 
model is used for the particular member. 

Table 5D - Nonlinear Member Support Curves 

T,hio M !r ber u SUPP ° rt CU u rVeS (q_w) are in P ut similar t0 the Q-W curves of 
able 4C. However, the final q values will have the unit of force per 
unit distance. K 

nf nn ? 6 +c q " W ^ rves at both joints of a memb er must have the same number 
member ^ inter P o1ation alon 9 the length of the 

Table 6 - Member Load Data 



Load types must be input in ascending order. If Table 6 is held 
from the previous problem then the first new load type in Table 6 (if 
any) must be equal to the number of load types in the last problem plus 



one. 



^ T f un he , H ° ld ° ption for Table 6 is set ec l ual t0 tw ° (2) in Table 1 
then l able 6 must have one statement for each old type, which has the 

f 0d 1 iTo^ H the Pe K rC r^ {2 l PerCent = 25 '°> increase P 1n' absolute va 

a\ Joads described in that load type, plus whatever statements are 
needed to define any new load types. 

Load types with only uniform loads over the full member length may 
be input with only one statement. Other loadings require two or more 
statements. 

If more than one statement is used to describe a member load type 
the uniform loads on the first statement must be left blank. 



Variable, concentrated, and partial uniform loadings must be input 
iLbn iLcf need _ not be input consecutively, and sections may 
overlap. This format is illustrated later in this appendix. 



197 

All sections, except concentrated loads, must have their TO 
distance larger in absolute value than their FROM distance by more than 
the length of one discrete element. 

Concentrated loads may not be specified at a distance of 0.0. 
Table 7 - Iteration Control 

The maximum number of iterations for the frame and member solutions 
should be specified to save computer time. Normally, convergence will 
be reached within five or ten iterations. An upper limit of 20 is set 
in the program. 

The allowable equilibrium errors may be set by the following 
procedure until the user develops his own special requirements. Select 
as a force and a moment that would have a negligible effect on the frame 
if applied at any point in the frame. (For example, the desiqner may 
know the value of his loads to the nearest 0.1 kips. Then a reasonable 
joint force error would be 0.01 kips, and a reasonable moment error 
would be 0.01 kips times the length of a typical member.) The errors 
permitted in the member solution should be 0.1 times the corresponding 
joint errors to allow for round-off. 

Monitor joints and members options may help to study the iteration 
process, particularly if the solution fails to converge. The numbers of 
the monitor members are the ones assigned by the program in the order in 
which the members are input in Table 3C. In a dynamic problem, 
hysteresis information will be output for monitor members only, and the 
time history of displacements and shear moments will be printed and 
plotted for monitor joints only. 

A maximum of 20 monitor joints and 20 monitor members can be 
specified. 



0) 



198 



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APPENDIX D 
JOB CONTROL LANGUAGE STATEMENTS 

This appendix presents the data sets (files) involved in the 
FRAME82 analysis of frame structures. FRAME82 analysis requires 
sequential data sets. The data sets can be stored in either magnetic 
tapes or di rect -access storage devices. However, direct-access storage 
devices of disk type are recommended for the FRAME82 analysis since they 
require less access time than the magnetic tapes. Cards may be used for 
the units that store the hysteretic response of the structure subjected 
to dynamic loading. 

The program, FRAME82, requires four scratch files and three 
permanent files. Three more permanent files are required if SAVE option 
is to be specified in the analysis. Cards may be used as the storing 
device for those additional permanent files, since the member and joint 
hysteresis output stored in these three units need not be read during 
the execution. 

Scratch files 1, 2, 3, and 4 are used to transfer member results 
back and forth from the core during a run. This reduces the memory 
requirements for member results to that of a single member since the 
results of only one member are held in the core at any time. Cataloged 
(permanent) files 11, 12, and 13 are used to store the results of the 
entire frame; i.e. joint and member results. Cataloged files 14, 15, 
and 16 save member hysteresis at the FROM and TO ends in the direction 
of original geometry, member responses at the sections near to the FROM 

200 



201 

and TO joints in the direction of deformed geometry, and joint 
displacements and joint shear moments about the z-axis, respectively. 

The results are alternatively written on to files 1 and 2, 3 and 4, 
and 11 and 12 on successive steps so that there will be at least a 
complete set of good results in the case of convergence or power 
failure. File 13 keeps the information about which of the two files 11 
and 12 contains the latest complete set of good results of the frame 
analysis. 

At the end of each load increment or time step, if a successful 
solution is obtained (i.e. member and joint solutions satisfy the 
prescribed equilibrium errors), the member and joint solutions and 
related quantities are written on to permanent files 11 and 12. Member 
solutions and related quantities are stored in scratch files 1 and 2. 
However, the joint information remains within the core and requires an 
insignificant amount of space compared to that of member information. 
Therefore, usage of same space parameters is suggested for files 1, 2, 
11, and 12. Files 3 and 4 store the indices for various sublayers of 
the discrete elements and for member support curves to keep track of the 
occurrence of strain reversal. Since the Input/Output operations are 
very small, files 3 and 4 do not need large space as files 1 and 2. 
Nominal size space is adequate for file 13, since it contains only the 
number of the unit which stores the latest complete set of good results. 
Files 14, 15, and 16 are required only if SAVE option is prescribed 
and their sizes are depended on the number of time steps. Refer to the 
WRITE statements in subroutines DYNA and DYNAJS to compute the space 
requirements for these files. 



202 

The example problems solved in this study were run on IBM 3081 in 
conjunction with IBM 3033 and IBM 4341 as supports in a 3 cpu 
environment. The JCL statements used in Example 9.2 are listed below 
(6, 47). 

//EX92 JOB (2006,0800,400,20,0), 'V.BALACHANDRAN',CLASS=1, 

// REGI0N=1000K,TYPRUN=H0LD 

/^PASSWORD 

/*R0UTE 

//STEP1 EXEC PGM=FRAME82 

//STEPLIB DD DSN=UF.B3060801.S1.FRAME83,DISP=SHR 

//FT01F001 DD UNIT=3380,DCB=(RECFM=VBS,BLKSIZE=23476) 

// SPACE=(TRK,(03,01),RLSE,C0NTIG) 

//FT02F001 DD UNIT=3380,DCB=(RECFM=VBS,BLKSIZE=23476) 

// SPACE=(TRK,(03,01),RLSE,CONTIG) 

//FT03F001 DD DCB = (RECFM=VBS,BLKSIZE=5492,BUFN0=1 ) 

// UNIT=3380,SPACE=(TRK,(02,01),RLSE,C0NTIG) 

//FT04F001 DD DCB=(RECFM=VBS ,BLKSIZE=5492,BUFN0=1 ) 

// UNIT=3380,SPACE=(TRK,(02,01),RLSE,C0NTIG) 

//FT06001 DD SYS0UT=A,DCB=(RECFM=FA,LRECL=133,BLKSIZE=133) 

//FT11F001 DD DSN=UF.B3060801.S1.BALA11,UNIT=3380, 

// DISP=(0LD,KEEP),SPACE=(TRK,(03,01),RLSE,C0NTIG), 

// DCB=(RECFM=VBS,BLKSIZE=23476) 

//FT12F001 DD DSN=UF.B3060801.S1.BALA12,UNIT=3380, 

// DISP=(0LD,KEEP),SPACE=(TRK,(03,01),RLSE,C0NTIG), 

// DCB=(RECFM=VBS,BLKSIZE=23476) 

//FT13F001 DD DSN=UF.B3060801.S1.BALA13,UNIT=3380 

// 0ISP=(0LD,KEEP),SPACE=(TRK,(1,1),RLSE,C0NTIG), 

// DC6=(RECFM=VBS,BLKSIZE=20) 

//FT14F001 DD DSN=UF.B3060801. SI. BALA14,DISP=(M0D, CATLG) 

// DCB=(DS0RG=PS,RECFM=FB,LRECL-80,BLKSIZE=23440) 

// UNIT=3380,SPACE=(TRK,(35,05),RLSE,C0NTIG) 

//FT15F001 DD DSN=UF.B3060801.S1.BALA15,DISP=(M0D CATLG) 

// DCB=(DS0RG=PS,RECFM=FB,LRECL=80,BLKSIZE=23440) 

// UNIT=3380,SPACE=(TRK,(35,05),RLSE,C0NTIG) 

//FT16F001 DD DSN=UF. B3060801. SI .BALA16,DISP=(M0D, CATLG) 

// DCB=(DS0RG=PS,RECFM=FB,LRECL=80,BLKSIZE=23440) 

// UNIT=3380,SPACE=(TRK,(16,04),RLSE,C0NTIG) 

//FT05F001 DD * 

/^INCLUDE DATA 

CEASE 

/*E0J 

If the permanent data sets do not exist in the system at time of 

first run, the files 11 through 16 have to be created using the 

disposition parameter DISP=(NEW, CATLG) . For subsequent runs, 

disposition parameter needs to be changed to DISP = (OLD , KEEP ) for files 



203 



11, 12, and 13, and DISP=(M0D,CATLG). for files 14, 15, and 16. Use the 

following DD statement for files 14 through 16 if the member and joint 

hysteresis is to be punched on cards. 

//FTnnFOOl DD SYS0UT=B,DCB=(RECFM=FB,LRECL=80,BLKSIZE=80) 

Refer t0 System/370 Job Control Language by G. E. Brown (6) for further 

information regarding the JCL statements. 



APPENDIX E 
GLOSSARY OF FORTRAN VARIABLES IN FRAME82 



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APPENDIX F 
FORTRAN LISTING OF FRAME82 



CO«« £ »T fiiii AIS PBOGBAM J£ FBAHE82 

B£AL*8 JTSHB * ' 
fi£AL*4 DISJT 

FOECEL, STBANL, BHOHNL, 
POECEB, STBANB* BBCMNB, 
FEHAXF, FBMAXd" FEilHCfl' 
fOAXF, TOAXD, TOHCH, 
5HHJT 
mS I ^ T , D S IVEfi 0SLY DIMENSIONS pfiOGBAM 
TO CHANGE DIHENSIORS CBANGE OHLI THIS DRTVFR 
S2Sf?Ii 8 l Sf B- 1 * A"8CPEIAT£ SDBBOaTINES EE 
VAEIABLE NAMES DO NOT CHABS| IB DIMENSIONED COBMON BLOCKS 



EEAL*4 
2 

3 

4 

5 
COMMENT 
COMMENT 
COMMENT 
COHHENT 
COHHENT 
COHHENT 



COEVAL, SHFOHL, GAflfiAL, 
^OBVAB, SHFOBB, GABMAflJ 
FEBaOT, FEHSBF,FBHLTD, 
TCBOT, TOSHF, TOLTD, 



AND DIMENSIONED 



_ *+****************#*., # * + 



- £M(Lb,L4) EOCL6) 

COHHENT - DEi«jf (4*HNJT) l ' 
COMMENT - COMMON ULCCK1 (BNJT) 
COSH|NT - COMMON BJ.CCM ,'HBH) ' 
COMMENT - COHHON BLCCK7 L1) 
COMMENT - COMMON BLOC 1 I MNJT) 
COMMENT - COMMON SLCC10(4,L4{ 
COMMENT - COMMON BLOC1 V BNQiH) 
COMMON BLOC21 i 4*gNJT) 
COMMON BLOC22|HNJT) ' 



m* 90 

00003*63 

00004 

00005*82 

00006*82 

00007*88 

00008*88 

00009*88 

00010 

00011 

00012 

0Q013 



DIMENSION CTlSi ***"******£*i*******00014*90 



«(i6} 



COMMENT 
COMMENT 
COMMENT 
COMMENT 
COMMENT 
COMMENT 
COMMENT 
COMMENT 
COMMENT 
COHHENT 
COMMENT 
COMMENT 
COHHENT 
COMMENT 
COMMENT 
COMMENT 
COMMENT 



MHTVJI,flNPTF) 



COMMON BLK9 

COMMON BLCK1 

COMMON SKT1(flNJS,10) 

COMMON SKT5 (HNE1/10) 

COMMON SKT7(HNE1) 



BLOCK2 (MNST) 
BLOCKS (MNC5) 
BL OCK8 (MN J S) 



BLCC12 MMCS,HNPCS) 

BLOC16(HNJT) 

(4*HNMJ.HNTST1) 



BLOCK3(MNLT) 
BLOCK6(MNC6) 
BLOCK9(MNPCS) 

BICC13(HNSS) 



BLOC23(3,BNJT) 



BNJT) 
10). 



i-unnifljL - LUHflON SKT7 (MNE1) SKT9fKNM fit 

E8SHH : iiSSSM mmn&:^J$ifl* V -™"> 



COMMON SKT14 
COMMON SKI16 
COMMON SKT22 



(HNE1,2,BNPCS» 6 



(ANTS! 



COMMON SKT30(flNST)S(HNII) 
COMMON SKT32 l '—'-* ■»===« 

COM' " 
*** 



SK1 19 
SKT28 



(BNH,6) 
(HNJT, 5} 
(SNHH,MNTST1) 

MON SKT32'7sNE^M > n'pCs'bSSIM1) S 
MON SKT33 (HNE1 '2, HNPCS) ' 



DIMENSION EM (100,24), BO (100).S( 100) 
DIMENSION DEXBJI (W 



COMMON /BLOCK1/ 1(25), 
SXX(25 
DZZJ25 



00015*90 
00016*90 
00017*90 
00018*90 
00019*90 
00020*90 
00021*90 
00022*90 
00023*90 
00024*90 
00025*90 
00026*90 
00027*90 
00028*90 
00029*90 
00030*90 
00031*90 
00032*90 
00033*90 
00034*90 
00035*90 
00036*90 

00039*85 
00040*85 



SKT2(HNJT,10) 
SKT6 (HNM) 
SKT9{MliM,6J 



SKT20 
SKT29 
SKT3 



HNE1,3) 



[HNE1, 
9 L1) 

1 (HN5S) 



(MNE1,2,MHPCS). 

SKT34 (MNJT) 



QZZ 
DYY , 

ERXX 
NSXX 
NSYP 






COMBOS /BALA0 1/ 

2 B7V'(2S), ' 

COMMON /BL0CK2/ 

2 DC2S( 25) , 

3 PEAG(25). 

4 IGPOP_^25), 

6 



EB1. 

NSxy]25l' 

ISTJfi(25J 

IVA\\\\ 

DXS( 25), 
PBFf 25) 
ELEMN(2: 
IPIKL( ' 



SYY(2§) , 
EXXJ255 . 
BBZZ(25), 



NSZZ(25) 



QXX(25) 

SZZ25 
BYT i 25' 
QHJ 25 
IMJ 25 




S7V<25), D7V(25), EB77 (25) , 



DYS( 25), 
PBAE( 25) , 



ZLS( 25) , 
QH( 25), 



DCISf 25) , 
BH( 25),' 

INLOPf 25) , 



25^, IPIHB( 25), NC51( 25) 
COMMON /BLOCK3/ DXL ( 25), DYLf 25) 7.T I I ?=!) nrni ?<;» 

i &miiv t mlm 8 «<^' ^^ ssisw 5 is,. 

2 COMMON /|LOCK4/ FOHH^O I) -»CJ50 jl^ISTJSO, ; 

COMMON >BL^K5/ XLS\ sb. XBS I 5J,'' jfl^fl' 



LI (50), 



SXL ( 50) , 
COflf.ON /BLOCS6/ 



^QZL'( 75) , 



COHHON /BLO 

2 SZ( 22) . 

3 DY( 22$ - 
I SQX( 22) 

5 HTf 22). 

6 BMTSf 22 
COHHON /BLOC 



V 



SYL{ 50) , 
XLLJ 75$, 
IOVH\l(75) 



SZL 
XBL 



50 
75 



«.J/ NPT( 2 0) , 
2 NQJT(11), NiijiMl) 

COBMON /BALA09/ GL(IO). 



DZ { 

soil - 

BM2S( 22), 

NPT( ~ 

N8J1| 



AE: 

Qll 

EEX 

SQZj 22 

72 ( 22)' 

TIS( 22) , 

I3J( 20), 



IMC (50) 
AEL( 50) , 

QXL( 75), QYL( 75), 

SX 

QZ 
ER 
01 
S2 
AG 
NQ 



!/ 22) , SX( 22) , SY( 22) , 

■1,221. QZ 22L' DX 221 1 

:| 221, ||i (22f. EBZ( 22/ , 



II 



22) , 

22j . 
22 
2D,11),NBJ( 20,11), 



71 ( 22) , 
DS{3,3, 



22) 



B»it ftf 



DBCL(1i 



COMMON /BLOCK9/ Bc£(l6[, 
2 YCL(10). DYc£(l6f. SIGl|iO,1i). 

depsl (i6, u), zssinbf. nsslhc \\' 

COMMON /BLOCl/ ZMASS (25) ,FTMJXX (25) ,FTMJ 

FTMJVV(25),TTMJ(i5),NFIXX(25),ilFTYY 
COHHOK /BLOC10/ SSL (4 A,: - l ' ' 

COHMON /BLOC11/ SEE 
COMMON /BALA 12/ SHC 



SHCLflO) , 
DCL(IO) 



DSHCL(IO) 
DDCL(IO) 



2 



3LJ4,24) 
5ET(6,6J 
ic720,1D 



<-L,llV). OUCLC1U), 00077 

£PSL(15.11) ,DSldL(l6, 11), 00078 

• NoSE ( 1 ) 

JYY(25) ,FTBJZZ(25) , 

(25) ,NFTZZ(25) ,NFTV7(25) 



COMMON /BL0C12/ SMtio.lO), 
2 11(20.10). NSSi26,l0f, 

COMMON /BALA 13/ GS (08) 

COMMON /BLOC13/ NPTS( 08), 
2 BSITMI) , NEPTi'11)' 

COHHON /BLOC14/ NPTH( 20), 



EM(20, i 
NA(20) , 



10) , BI(20,10) , DI(20.10) . 
NCDA(20), IEEdT(20,l6) 

ISS( 08), NSIG(08,11),NEPS(08,11), 

ISM( 20), NQM(20,11), NBM(20,11), 

SIGTS(11) 



SIGT(21) 



2 NQMT(11) . ' NBHThl)' 
COMMON /BLOC21/ ACCJT ( ioO) , VELJT ( 1 dO) .ZMASSB ( 100) ,DACCJT ( 1 00) , 



'(25) 



00041 

00042 

00043 

00044 

00045 

00046 

00047 

00048 

00049*70 

00050*75 

00051*42 

00052*42 

00053*42 

00054*42 

00055*42 

00056*42 

00057*79 

00058*80 

00059 

00060 

00061 

00062 

00063 

00064 

00065 

00066 

00067 

00068 

00069 

00070 

00071 

00072 

00073**5 

00074 

00075 

00076*48 

00077 



00079 

00080*82 

00081*82 

00082*75 

00083 

00084*51 

00085 

00086 

00087*50 

00088 

00089 

00090 

00091 

00092 

00093 

00094 

00095*75 

00096*85 



218 



219 



DVELJTMQQ) .FACCJJ 



2 



COHaON/BLOC2U/ AN1 (4o[ , A&2 (1 1) , NPBOB (2) oninilf 2 

2 AEEP2- KEEP3A,KEEP3E,KEEP4A,KEEP4B,KEEP4<5,KEEP5A 00103*61 

I ^2?f^,K£EP5C,KEEP5D;KEEP6, KEEE7, 'SCD2. NCD3A. 00104*61 

« NCS3B, NCD4A, NCD4B, NCD4C? NCD5A^ NCD5B. NCD5C 00inq*fl 

5 NC05D, NCD6, NCD7,' IP8, ' IP9, IP10. ITYPe' OOlolJIl 

COMMON /BLK4/ ST1,ST2,ST3,ST4.ST5,ST6 00112 9 

ccgsos /blk5/ nfsub.nitf.ni.nS nnill 

C^7«7»7,' WW'* 11 * ' Mix 

gggSSS *"«& l^i""" 4 | " 

S?2 l M ^ BB /. PCEML, PCEJL, NLB. NLEA 00124 

2 CCH ^L<fF%, g||4?ifc 1 ?l «'EY(2S,10?r°fiBZ ) (25 / 10 I , 00127*84 

1 !M.(25.1?), «5XP 25.1DJ, »BYP(2S.10). HBT2(2$.10f- Sni?als2 



I m\m%\ l ™™«y> ™w'.m-. mmm. mnn 

COMMON /3KT3/ NCCONT, NITEEF noi^i* 84 

COMMON /SKT5/ WBXB (21,10), WBYB (21,10), «EZM (21.10) 00132 

2 co H «on /sk.6/ M^'hoIF^ 2111011 ™Tz a (ii;?8!' || 

COMMON /SKT7/ 0112(21), V1TT(21), B1TT(21) OOlil 

2 C0MO./SKT8, lillijl V2 "^ HS88' 

C0»HQ| /SKT9/ EHDFda!5C.6) 

COMMON /SKT10/ NDIV (20, 16) , SPCTOK20) ooilq 

COHHOK /SKT11/ BSSlNL, BSSIH1 ' nniun 

COMMON /SKT12/ EPSIEL^OS, 03) , SIGBAX ( 08 . 03 1 00141 

COMMON /SKT13/ g£g j| li 1 A£\\ .EPBTlI J21 ', 1o',3) . 00 42 

COMMON /SKT14 / T R V f f^ 2 f ^ A f 1 ° ' 3 ' ' S PB T2 S < 2 1 ' 1 ° ' 3 00143 

CUMMON /SKT14 / IEV(21,2,10! , FO8OLD{50,6) , 00144 

2 CC«K0N /SKT15/ 55™"' IIAPE ' N3 8 3 1 SI 

c8SS8» ^ll? 1 1^ N4 * EXXOi <25),EEYYOL(25), E BZZCI.<25,,EBVVOL(25) 0°0 47*75 

COMMON /SKT18/ NCHECK 00149 

COSaOH /SKT19/ JCEGCN (25,6) , JCUEEV(25,6) 00150*84 

gggftf ^IlilH^ S?I« c Sigi- 3 > : «=D«T(ai:S| 8 8 || 
§8SS8i flgg* SSt!«A JT ' IHDYN - «■«»<«) o If 

COMMON /SKT25/ TTSLEF, 11SBGT, NLE, NEE 00155 

COKHOH /SKT26/ LTYPEL ' ' 00156 

COMMON /SKX27/ IBEAE, IWBITE 00157 

CCflhOH /SKT28/ FOSCEL (20,71), STBANL (2 0,71) .BMOBNL (20,71) , 00158*88 

\ C0RVaLfa0,71» #Igg?EH{20,7ll ,STBANH (20,7 1) , BM0MNfi'(2Q,7 1) , -00 59*88 

3 CUEVAfi(20,71) ,FEMAXF(20.71) , FEB AX D (20, 71) 'fBHHOM (20'7 1 ' 00160*88 

4 FSaEOll20.7l} FBM3HFJ20171 jFBHIlDho 1 7 1 J IOAXF (20 , 7 ' ) , 00161*88 
I TCAXD(^0,h), TOflOM (i0 # 71)'/lO8CT (20,71) '/TOSHF20:71 00162*88 

10^10(20,71) 00163*88 
CCMMON /SXT2S/ EPSLGN (22). CUBVA1(22), COEVA2(22) 00164 
COMMON /5KT30/ KSTIF(25), KLOAD(25) , flCDEL(25) 00 65 
COiSfiOH /SKT31/ ALPHA (8), BETA (8 , SMLSLP(8), EPSTHD(8), 00166 

1 SLOPED(8), SIG0LTJ8J' HATBI (8) 00167 
CCMMOK /SKT32/ EPBF1 2 S \ 1 0,3) , EPBFT 1 (21 , 1 (5,3) , SLBF1 (21,10,3), 00168 

\ %\\lV\\h\^'l\' 2EBF2^{21,10,3) , EPBFT2 Ul'lOjS , 00169 

} SLBF2 (21,10,3), SLBFT2 (21 , 1 0,3) , l ' " 00170 

1 |PSHAZi21,2,10l , 2P5MIN(21,2,10 \, EPSPBE (21,2, 1 0) , 00171 

5 IGECW (21,2,10), Y1GEOK (21,2,10$ 00172 
COMMON /3KT33/ NSG10N 2 1 !2 ' 10 ' ' ' 00173 
CcShOB ^IkT35^ iili??' 25 ^ Ea ^ DN < 25 »' EEZZDN(25), E B7VDN(25) 00174*82 
COMMON /GT/ MJO 00176 
COMMON /CHAN1/ JTSHE 00177*67 
COMMON /CBAN2/ SHMC(25) • 00178*82 
COMMON /CHAN13/ NPTJ( OS), JSSI 08), NTAO (08, 08) , NGAB (08, 08) , 00179*79 

2 NTAT(08) , NGA1(08) ' tAUMLT (08) ,GAMHLT(08) l ' " 00180*79 
COMMON /CHA15/ gXbie£ (08, 03)^ , tSoMAX(03,03) 00181*79 



ilfl* NGA1(08) , tAUMLT (08) ,G AMMLT (08) 

'CHA12/ GXMIEL(0a,03) , TAUM AX ( OS , 03) 

.'CHA13/ GABES(25,3) ,GAHBlS(25,3) ' ' 

CCIiMCN /CHA19/ JSV(25) ,JB6i0N(25) 00183*80 

2 C ° K ^M^B H t 2 2^7l) H Si^2C 7 ;7l) GA ^ AL ^ 88,11:11 

COMMON /ChUv AUgCgJ Jg^jjj. H^jSJ, GASTH D (8), | * 

CALL EBBS EI J 208,256,- 1, 1,1, 208 ) 00188 



HHJT = 21 

HHJST= 25 

MNM = 50 

MNMJ = 20 



00189 
00190*59 
00191 
00192*88 



220 



KNMB 
BNST 
MNLT 
HNC5 
MNC6 
HDJT 



= 5 



20 
25 
25 
50 
75 



mir 



88 



MHB = 4*BDJT ♦ 3 

MSB = 20 

JJNJS = 20 

MNJSS = 8 

MNCS = 20 

MNPCS = 10 

BNSS = 8 

MNTVJL =20 

MNPTF 

MNTS1P 

BNTSI1 

BNQWB 

MSSINL 

HSSIH1 

MNE1 = . 

LI = HUE + 2 

L2 = 3*MNE1 

L3 = MHB 

L4 = BHB ♦ 

L5 = 3*L1 

L6 = 4*BNJT 
IF (L6 .LI. L5) L6=L5 

LI = 3*L1 ♦ 1 
COMMENT - SUBEOUTINE STATIC IS THE MAIN S 
CCUaENT - AND PEBFOEMS SIfiPLE INPUT, GDTP 
CALL STATIC { EM, BO, U, SL, l\ 

END 



300 
= 70 

= BNTSTP + 1 
= 20 
= 4 

= mssini - i 

BNE + 1 



1 



00195 

00196 

00197 

00198 

00199*85 

00200 

00201 

00202*79 

00203 

00204 

00205 

00206 

00207*87 

00208 

00209 

00210 

00211 

00212 

00213 

00214 

00215*85 

00216 

00217 

00218*85 

00219*85 

00220*85 

UBSOUTINE OF PECGBAK FHAME63 00222 
DT, AND COMPUTATIONAL FUNCTIOHS00223 
, L2, L3, L4, L6,D£LSJT) 00224*85 

00225 
00226 



**« *->* ************ **************** stiRRnnT 

SUBROUTINE STATIC (EM, HO, B, SI, LI, 

S9SSIPJ " IP2O0TINE STATIc'lS THe'haIN SUB 

COSKBKT - STATIC CALLS PBIMAEY INPUT. CUTPO 

COMMENT - AND PEBFOEMS STATIC ANAIYsis. 

IMPLICIT 2EAL*8 (A-H,0-Z 

HEAL*8 BEHBEE 



SEAL*8 JISHE,JSY£S 
DI3SNSI08 SMMT(21) ,FOBT(6) 
DIMENSION SM(it>,L4), BO(L6), SI(L6) 

DIMENSION DELKJT ( L6 ) 

COMMON / # D|LK1/KEE?5D / »CD4D,KEEP4E,NCD 



IME ********************************* 
12, L3, L4,L6,DELIJT) 00227*85 

EOUTINE OF PECGBAH FBAME82 00228*90 
T,AND COMPUTATION SUBBOUTINES00229 

00230*90 

00231 

00232 

00233*59 

00234 

00235*74 



i-unnun /UBLM/siii'itu, 
COMMON /DBLK3/ MNTVJL 
COHHON /BLOCK1/ X (25) , 
2 QZZ(25), SIX (25), 

EEXX(25i. EBY_ 

NSXX{25). NSYY 



4E 



Lilt 
<(23l , 

Mtllf. 



o NSYP{25 , ISTji(25) 

COMMON /BALA01/ QVV(25», 

2 BVV(25), SSVV(25/ 

COMMON /3LOCK2/ DXS ( 25) , 

2 DC2S< 25) , PEF( 25[' 

3 PEAGJ25), ELE8K(25[, 

4 lOeoit 25) , IPINL( 25f, 

5 NAL( 25) , NSXL' 
NSXBJ 25). NSYE 



SYY(25) , 
EXX (25' 
EBZZ(2 
NSZZ(2 



If: 



QXX(25 
SZZ (25 
BYY 25 
QMJJ25 
IMJ(25 






SVV(25), DVV(25), 

ZLS( 25) 
QW( 25), 



DYS( 25), 
PBAE( 25) 



IPINH( 25 
NSYL( 25) 
NSZB 2 5 
(25),HLJ( 



.{ 25), I 
1 25), i 
cck.*:on /BALAD2/ JSI(i5),HJSS(25i;axj'( 
2 THKJ(25),GJ(25),SJC(25) l 

CCaflO* /BlOCii/ DXlt 25), DYL( 25), 

2 OCatl 25), UQX 25i; UQY 25 ,' 

3 NC6 1( 251, IGVHB(25) 
COfiiOS /BLOCK4/ FOKH[5Q,6) ,SBC(50,21) 



), 



NC51 . 

NSZLi 



25 

25 



, ilOiil £3) , OAK ^3), 

. NCDSf 25 , lAXOPSf 25) 
25),HEJ(25),VLJ(25),VdJ(25) , 



QYY(25) , 
DXX(25) , 
EZZ(25) , 
WMJJ25J, 
N5X]?(25}, 

EEVV(25) , 

DC1SJ 25) , 
»M( 25), 

INLOPf 25) 
NAB< 25) 



ZLL 

NCDL' 



( 25), 
L( 25), 



DCUJ 25) , 
IAXOPL ( 25) , 



JT1'(50) , 
.common /BLOCK5/ XLS 



JT2(50) , 
XLS 50) , 
2 SIL( 50) , SYL( 50) , 

COaaCh /BLOCK6/ XLLl 75), 

4 QZL ( 75) , IOVKL(75J 
CCMfiON /BLOCK7/ "' 

2 S7 ' 

3 Dl 
4 

5 tfT(*22)' 




NITM(50 
X£S ( 50 
SZL 50 
XEL( 75 

AE 

QY, 

EBX( 22), 

SQZ( 22) , 

TTS< 22/, 



,IST(50 , LT(50), 
) , 188(50) , IMCY50) 
FL( 50), AEL( 50) , 

QXL( 75) , QYL( 75) , 



ccaaoN /ealaid/ ebvvmj (5,25) ,dvvmj (5, 

COfiMON/ELOC24/ AN 1 (40) , hli2( 1 1) , NEEOB 

COEJIOS /5LK1/ TOL, ELEMNT,NJST, K 

4 KEEP2, KEEP3A,KEZP3E,KEEF4A,K 

3 KEEP5i,KEEP5C,KEEP5D,KEEP6, K 

4 NCD3B, NCD4A, NCD4B, NCD4C, N 
b NCD5D, NCD6, NCD7, IP8, I 
6 IABAN, IFGS2, Na, SJT, N 
1 MP1, KP2, IS11, LTT, I 

CCaaOK /3LK3/ 3KJT,aNST,*NLT, MNK,BNC5 



SX ( 
QZj 
EEY 
U1 
W2 
AG 
TBJYY 
YY(25V 
25), E 

KOB 



II; 



SY( 
DX( 

E5Z( 



22) , 
22). 
22) , 




22 
22 

( 22 2 

22 

22, 
25) ,FTHJZZ(25) , 
,NFTZZ(25) ,NFTVV 
BZZBJ(5,25) , 
J(5,2£),KOJ(25) 



V1( 22) , 
DS|3,3, 22), 



(25) 



NCD3C, 

KEEF4C,KEEP5A, 
NCD2, NCD3A, 
NCD5E, NCD5C, 
IP10, IIYPE, 
KLT, a, 
IDJ, NSTL 
KDJT,MNJS,MNE,MNCS, 



00236 

00237 

00238 

00239 

00240 

00241 

00242 

00243 

00244 

00245*70 

00246*75 

00247*42 

00248*42 

00249*42 

00250*42 

00251*42 

00252*42 

00253*79 

00254*80 

00255 

00256 

00257 

00258 

00259 

00260 

00261 

00262 

00263 

00264 

00265 

00266 

00267 

00268 

00269**5 

00270*82 

00271*82 

00272 

00273 

00274*75 

00275*56 

00276*79 

00277*61 

00278*61 

00279*61 

00280*61 

00281*61 

00282*61 

00283 



221 



LLMMON /HAiiiV NJNC.NMNC 
COMMON /NIT/ APfioV 



«ETY?(25,10) 

COHMON /SM3/ NCOU 
COMMON /SKT5/ 



NT, NITEBJ 

WRXM ' 

KETXH 

KIT£fi_ 

MSSINL 



vU&h^lt "82(25.10). 
oi?Uif'35f» »HTX(25,lM, 
SEIV(25,10}, SRTXP(25, 1&f, 



(21,10) , 
(2l'l0j ' 
M5fi) ,'lN 



DEX 
HSSIM1 



COB&OS /SKT6/ 
COMMON /SKI 11/ 
COhMON /SKT13/ 

COMMON /SKT14 / m]!"! j? I)] *'•** * IIS5 

COMMON /SKT15/ "^J*" IIAPE ' 

COMMON /5KT17/ N4 

COHMON /SKI 18/ NCHECK 

COMMON /SKT19/ JCBGCN (25.61 lrnuFi/^"; ti 

SS8S28 /SKT20; MCBGCn|21:!|; BcglUg^} 



WBYM (21,10), 
«BITH(2i;i0J ' 



(21,10) 

i (21; ioj 



JiRZM . 
BHT2H(21, 10) 



FP^f^H8'^' EpfiT1s (21,10,3), 
^ fi2 5(2l,10,3) ,EPB12S(21 Jlo'3J 

FDfl 



S3 



MOLD(50,6), 



12 FORMAT 

13 FOE MAT 

14 FOEMAT 

15 FOaMAT 

16 FORMAT 
22 FGBMAT 
30 FOEMAT 

2 55U 



EPBF2 (2i;io;3 
5LBFT2 (21,10'3 
EPSMIN/21,2,1o 
ITGBO»(21,2^10 



-TEI.1 ) 



SLBF1 (21,10,3), 
EPBFT2(2i;i0'3J; 

EPSPB2(21,2,10) , 



COMMON /SKT23/ PCEI1A 

COMMON /SKT27/ IEEAE, IHBITE 

J SLBF2 [gliiojj 

I £?SfiAX(21,2,^0 

5 CO"*M /CHAIV J?Igg < 21 ' 2 ' 10 
COMMON /CHAK2/ SHMC(25) 

COidEON /CHA13/ GAMES (25.3) GAKETSfPS 1\ 
11 PciSS? 'WS JEV(25f,5BGt0N?25f <25 ' 3) 
T JoA4) ' * ' 10HI -— L 

A4.A1 .A4,A1,A2,17A41 
/3V/ i, ',^S» ^' 2A5,7A8,A4) 



*5"£ »//#-?A»Ai|, A],A4, 1X.2A5.7A8 A4l 

PBCB (COHTD) ,/;5x;A4',A i; lOX.'AS^AsUa,///) 



( U, 20A4 ) 
t/A /8J1H-) ,//, 

NOTE - THIS PROBLEM ANALYZED EXCLUDING ALL GECMSTHIC / 

- THIS IfiopiEH ANALYZED 2|CLa D ING„ALL_GECMETBIC ,/, 



.4 42H 



3 57H 

4 56B 

5 20H 
5 FOEMAT 

2 



(/A SO 



KiiiiHSiTiSS-r*XK peige Celebs this PBCBLF^ 

THE FOLLOWING CARDS WERE, 



3 2P * ** « ** w wtif JUUULU ti fi V 1L DI 

£DUO OPTION./.78MH-),//) 
| SOLUTION ABANDONED 



2 ""15b DISCABDED7//) " , ' Ua * U ~ 1UJS fULLCBIKG CARDS WERE, 

.^FORMAT (/A50H NO HOLD OPTIONS MAY BE EXERCISED ON FIRST PRO, 



S3 FORMAT 

99 FORMAT 

100 FOEMAT 

1C1 FORMAT 

2 



[ ///'A 



3 

4 
5 
6 
b 
6 
6 
6 
6 
6 



10X, 
10X1 
10X, 

iax,5tf 

10X,5E 

10X,5fi 
10X,5H 
10X,5H 
10X,5H 
10X,5fi 
10X,5H 



( 4 l/X' 3 ->H TABLE 1 - PROGRAM CONTROL DATS / 

45H TABIl 0BLE So?P^a^<<<S 2 " X '° 2 "^ U ""B{ES,// f 

<»5H. .. (1 = YES.O = 

10X,, 

10X,5H 

10X,5H 

10X,5H 

1GX,5H 

10X,5H 



■ «.i&a2Pi£!Sl 



3B, 10X,I3;i5x;i3,7; 
4A,10X,I3,15x;i3^/; 
4C,10i,I3;i5x'l3;/; 

4c,iox,i3;i5x;i3;/; 

SB, 10X,I3,15x'l3!/' 

5D,iox;i3;i5x,'i3;/; 



ADDED FOB THIS '/' 
PHCBLEB '//, 
3A,10X,I3,15X,I3'/, 

4B,iox,i3,i5x;i3;/; 
ip, ox,i3;i5x,i3,/; 

5A,10X,I3,15x;i3;A 
5C,10X,I3,15X,I3,/, 



10X,5H 7,10X,I3,15X,I3,/////) 



102 FOR a AT X '(2^X,13° H( 5^I„T 3 fl!!li^; 

103% C R«l? X ^?v „i^lAl ! ^ &L g|'5| 9.10x!f3C/,10X,5H 

1IHESTEP INTERVALS,/, 

2 10X, 7K TABLE,/, ' 

-i 10X, 7H NUMBEE,//, 



10X,28H TAELE' 
10X,24H NUHBEB 



10,10X,I3) 



10, 10X,I3) 



153 FCeHXt (ix 3 1H*,I4"'(1PE1^7) 5 ;3^plll U 3 

154 FOBHAT I/A47E' i I NDIC AIeI ' JOINT SDPi 
.ec^»- 2ufl END OF THIS PEOBLEM) 

155 FORMAT (///30E „„«*** FRAME ItILtICN NO .I5.6H *****,//, 

£ 5X, 43H 8EHB MEMB ciilMBEB DISpLaCEMEHTS 



??OET OFF C-W CUEVE AT, 



m^ 79 

00286 

00287 

00288*88 

00289*88 

00290 

00291 

00292 

00293*84 

00294*84 

00295*84 

00296*84 

00297 

00298 

00299 

00300 

00301 

00302 

00303 

00304 

00305 

00306 

00307 

00308 

00309*84 

00310 

00311 

00312 

00313 

00314 

00315 

00316 

00317 

00318 

00319*62 

00320*82 

00321*80 

00322*80 

00323 

00324 

00325 

00326*59 

00327*59 

00328*58 

00329 

00330 

00331 

88^3^*87 

00334 

00335 

00336 

00337 

00338*87 

00339*77 

00340*77 

00341 

00342 

00343 

00344 

00345*79 

00346*e7 

00347 

00348 

00349 

00350 

00351*79 

00352*79 

00353*79 

00354*79 

00355*79 

00356*79 

00357*79 

00358*79 

00359 

00360 

00361 

00362 

00363 

00364 

00365 

00366 

00367 

00368 

00369 

00370 

00371 

00372 

00373 

00374 

00375 

00376 

00377 

00378 

00379 



222 



| 11X, 258 KEHEEE . 



EqULIBEIDa.EHBOSS,/. 



00380 
00381 



CF FRAHE, 
j|p]x| EISP(Y) EOTATIOMZ) 



183 f0J8Bil(5X,!|*;f3.i£ IX fin 3» 



Q-8 C0HVE FOE, 



1SI THAI ITESAIICnT JCIHT SUPP0BT 0Fr 
185 FOMAT f^ gB ^** 15 3||^H«B| S HOT CLOSED AT END OF «««. 

200 FO 
21 



tiii enrag* w rcift pi ml wwa* ssi 



00382 
00383 
00384 
00385 
00386 
00387 
00388 
00389 
00390 
•t„_ K -, 00391 
JOINT EQUL, 00392 

BRH(X) ER, 00394 
00395 
00396 
00397 
00398 
00399 
00400 
00401 
00402 
00403 
00404 



1, IN THE ABOVE TABLE) 
IF? HE JOINTS i¥? l 22??„5 H S A . fi D«CHM A1IOM./, 



•0 FORMAT ( 80 ME-I .//) 

9a sots - lais analysis INCLUDES SEEAB DEFOB1ATICN / 



,//,5X, 



c/*«fcWifitf 



3 56H 

4 44H 
220 FO 

2 4 

3 5 

4 49H 
5 

231 FORBAT 

2 60H 

3 33H 

23 JJp.r 

233 FOS_. 



/ ]^TMT'p»j^ ; " JflI,ABy 0F FEAa2 IIFEATICHS 
OUIN1 FiiAttE JOINT D 7<?PT iriapwc 

OH N n JC ?^ C £fiD ^i B&IUH EBHOES D ;^ LACEKE ^ S 

)SaAT(5X,5H*,f3rf4,1Z*8£11 3> 



BO, 



23 5 5 rg|f AX S J K l5J H W) xSP43WTi:^> 6MPI1I 31 1 



. (65l,4(llg 
//, 65X'4J11H 



238 FOEfiAT (SX, 34 HIABLE 10 

3 Hff&tifttefrgHiJZL. 



OTAL,4 (1PE11.3) , 



777 FOBMAT ( 
2 

COMMENT - SET 



>6i^5HTC 

JSvULl 



JOINT 



4§H " *** 
10H DATA *** ) 
CONTBCL CONSTANTS 
DATA ITEST1, PRINT 
2 / 4HCSAS, 4HRIN1 / 

DATA aEaBEE /4KHEEE/ 
DATA PDNO /4HPDNO/, PDN/4H PEN/ 
DATA JSYES /5HJSYES/ ' 

DATA SHEAR /5HSHEAB/ 
I2EAE =11 
I»EITE= 12 
ITYPEL = 
N1 = 2 
N2 = 1 
N3 = 4 
N4 = 3 
KSETED = 
KSETJS=0 
. QaK ENI E - D aEAD RON 1 ID PRINT = P B OGH AH ID AND BUN I) 

PRINT 11 ' ' 

PEINT 22, { ASI(II), 11=1.40 1 

C °1$FL~* n m U kl$M & TO J BEAD hu PROBLEM 
1010 BEAD 14, SP50B, PDEL, JTS3B , (AN2 (II) .1 1=1 . 91 
IF NPROB ='CEASE, TEfisf SA TE ' RoV 



EQOLIBHIOa EEBOfiS,///, 
9X,( ' 



10X,6HERR(Z 
., i i Ji,ooQunii«T,9X,6HHOH 
SOLUTION DID NOT CLOSE 



l §ta 



/, 



X BONITOfi, 



COMMENT 



COMMENT ? _I2jPU/T_AND ECHO FBlliT PBCGEAM. CONTROL DATA (TABLE 1 



1050 PBINT^I ' CB5B ' HCB5C ' HCD5D ' N£D5 ' NC67 

1 .08. ITYPE -E 



00406 

00407 

00408*59 

00409*87 

00410*59 

0041 1*87 

00412*59 

00413*87 

00414*59 

00415*59 

00416*87 

00417*75 

00418*75 

00419*75 

00420*75 

00421*75 

00422*75 

00423*75 

00424*89 

00425*89 

00426*89 

00427*89 

00428*89 

00429*77 

00430*77 

00431*89 

00432*77 

00433*75 

00434*75 

00435*75 

00436 

00437 

00438 

00439*78 

00440*78 

00441 

00442 

00443*59 

00444*78 

00445 

00446 

00447 

00448 

00449 

00450 

00451 

00452 

00453*59 

00454 

00455 

00456 

00457 

00458 

00459*59 

00460 

00461 

00462*59 

00463 

00464*79 

00465*79 



S ) GO TO 1060 ° 0468 ' 



( ITYPE -. 
TO 1100 



:y. 



IF 

GO _ .. 
1060 CONTINUE 

IF ( KSETED 

PDELIA = PDEL 
KSEIiD = 1 

IF ( PDEL.EQ. PDNO 



.VS. ) GC TO 1090 



■OS. PEEL. EQ. PEN ) GO TO 1070 



00469 

00470 

00471 

00472*59 

00473 

00474 

00475 



223 



£* Ci Tn 1 A Q A 

1070 CONTINUE 80476*59 

CCSSII? : FEESH l°V 5 ifAENING HESSAGE AT THE BEGINNING OF & 88*78 

Pfi i K | F 3(J ITYPE - EC - 9 ' 30 IC 1080 88518 

50 TO 1090 00481 

1080 CONTINUE 2P, 48 ?* 59 

PEINT 35 00U83 

1090 CONTINUE 00484 

IF ( filial - HE - ° > GC TC 110 ° ootlltll 

IE ti TS ^k SQ - JS ™ 5) G0 I0 1095 SoSs 5 ! 

1095 CONTINUE SP^ 89 * 59 

gftgflf -" SBlirfSSM b a a !HI§ gSP 1SE AB0UI THE J0IBT SBEAfi AI *« llMlf*!! 

PBIhSMo 1 "" ' £Q - » » «> » «" 0°0°4 4 9 9 §:il 

GO TO 1100 00494*59 

1C98 CONTINUE 00495*59 

PEINT 220 00496*59 

1100 CONTINUE 00497*59 

FEINT 22, ( AN1(II). 11=1 40 1 P9??, 8 , 

IF 7 ITYPE .ST. 2 J GO TO 1126 XnlXS 79 

PEINT 102, IPS, IJ?9, IP10 00505 

„„„„ GO TO 1150 * 00506 

1120 IF ( ITYPE .GT. 4 ) GO TO 1140 nRIPZ 

PEINT 103, IPS, IP9, IP10 00508 

GO TO 1150 00509 

1140 PFiINT 109. IP6- IP9 IP10 00510 

1150 CONTINUE ' IP ' IP1 ° 00511 

COMMENT - CHECK FOE KEEP OPTION CN FIRST P30BLEM OF BUN 00511 

i £111,.^ , KEEP2 + KEEF3 A+KEEP3B+KEEP3C + KEEP4A + KEEP4B+KEE^4C + 005lil*7q 

IF < PfSS£ + K fP^ K fS* 5A *Kif"g*K2M5c™ 005 5*79 

ro in inn * E£> ° * A1,C - KEKE ' KE - ° ) GO TC 1200 00516 

1200 PEINT 51 00517 

COMMENT - ABORT PROBLEM, SEAHCH FOE INDEPENDENT P20BLEH 00519 

1300 CONTINUE 00520 

$£28111 " £ A 2 A ?„ = 1 INDICATES FATAL EEEOE FOUND IN SUBBOUTINE 0057? 

COHHEdT - PEOBLES ABANDONED IN SEAHCH OF AN INDEPENDENT PEOBL EH 00523 

IABAN = n „r,„ 

COMMENT - MAIN PECGEAd STAETS HEBE nnkll 

PRINT 11 PiPI 2 ^ 

PEINT 16, NPBOB, (AN2(II) ,11=1,9) nnWa*** 

cojiaENT - subroutine JTCOfiD INPUTS JOINT GECHETBY DATA (TABLE 2-\ nc\%?% 

CALL JTCOBD Anci-so 

IF ( IABAN .EC. 1 ) GO TO 9805 Oflfl? 

TEMP = KEEP3A + KEEP3B + KEEE3C 00534*79 
TSOPP = NCD3A + NCD3B + NCD3C 005}5*7q 

-0 ? TC$ 1420 ,HE * ° ,AND ' IEMPP ' EQ - ° > GC T0 1410 00536*59 

1410 PEINT 200 Pi SIR 2 

GO TO 1430 nnila 

1420 CONTINUE 82i|f 

PEINT 11 00540 

1430 PalS ?OHTf"oi° B ' ( * H2{II) ' I1=1 ' 9) 00542*55 
CO"« E «l ; SUBBOUTINE BEMLCC INPUTS LOCATION OF MEHBEB STIFFNESS AND LOAD00544*90 
LuOflEftT - TYPES IN FRAME, AND JOINT DATA AND JOINT SHEAS qTSP^<!-<;TPiTV nn^ii^*on 
CgMf" ~ CUEVES FOR ANALYSIS TEAT INCLUDES JOIHT SHEAS DEFOEbItIOH*" 00546*1o 
CUEHEL1 - aiFECTS (TABLE 3). ALSO COMPOTES MEMBER NUMBEBS, LENGTHS, EIC.00547*90 

IF ( IABAN .EQ. 1 ) GO TO 9805 00549 

TEHP = KEEP41 + KEEP4B + KEEP4C + KEEP4D + KEEP4E 00550 

TP , ll^J = «CD4A + KCD4B + NCC4C + NCD4D + NCD4E 00551 

GO io 1450 ' IEHPP ' EC * ° > GC TC 144 ° 00552 

1440 PEINT 200 P2tt£ 

GC TO 1460 nftllS 

1450 CONTINUE noil^ 

PEINT 11 U ^DDD 

PEINT 16, NPBOB, (AN2 (II) ,11 = 1,9) 0055R*55 

I4o0 CONTINUE v " ' ' nniio 

COXHENT - SUBROUTINE JSTDAT INPUTS JOINT LOADS AND EFSTEAINTS nnZZn 

C°MSENT " (TABLE i». CHECKS FOB BAD MTA.ACCUaULATES JOINT LOADS AND 00561 

COMMx.NI - aBSTEAIKTS.ECBO PRINTS DATA AND PEINTS ACCUMULATED DATA 0n5«9 

COMMENT - EQUILIBRIUM EEHOBS ABE SET EQUAL TO NET JCINTLCADS™™ 00563 

If ( IABAN .EQ. 1 ) GO TO 9805 00565 

IF ( NLH .NE. ) GO TC 1500 005ftfi 

TE3P = KEEP5A + KEEP5B + KEEP5C + KEEP5D 00567 

TEMPP = KCD5A + £CD5B + NCCSC + NCD5C 00568 

rl i>n I2 5In' NE " ° • AND - IEHPP * E 2- ) GC TC 1470 00569 

1470 PEINT°200 U8 ° 00570 



224 



,,._,, GO TO 1490 
1480 CONTINUE 
PRIST 11 

1490 PEIN COi }iiinl° E ' (AN2 (II) ' II=1 ' 9 » 

§S9H9| : ffiSSFiSI ISPLiiT^E^fiJii'KiS 8 DATA < TAB1E 5 >- 

CAitL ECKST 

I| ( IA6AN .20. 1 ) GO TO 9805 

go to E 5io mEQ ' 1 * ANE * NCD6 " EQ * ° } G0 TC 150 ° 
1500 PBINT 200 
,_„ GO TO 1520 
1510 CONTINUE 
PBINT 11 



.1520 ""SoilrfSI OB ' (A " (II, '"" 1 ' 9 » 



^ i 

IF ( lAi 
IF ( Nil 
IF JKEE! 
GO TO 1! 



rn«2f!I " faBfiOOTINE EDMLE INPUTS HEHBER LOAD DATA (TABIE 61 CHF( 

£83681 : ^o a fi Ei A ^T D !I A A N c D l ca TlE^T A s DS E ^S DISTA * CES 1 ™***&* C5ECKS 

IA3AS .EQ. 1 ) GO TO 9805 
NLH .SB. ) GO TO 1560 

xO E ?54C EQ *- 1 * Ai " D * KCC7 ' E0 --° 'AND. ITYPE.EQ.9 ) GC TO 1530 
1530 P£INT"200 

GO TO 1550 
1540 CONTINUE 
PHIHT 11 

1550 »" a s jfrfH 0I -< Ma ««>*»-i.»> 
gSSHSi : il^FLFFdZ HUH 5I?r TMH C0NTa0L DATA - CHECKS ?0E 

CALL ITCCNT 

GO TO 9 805 
GO TO 1560 



( IABAN 
( ITYPE 



•EQ. 1 ) 

.NE. 9 [ 

= ITYPE 



IF 
IF 

ITYPEL 
,_,„ GO TO 1010 

1560 CONTINUE 

IF [ ITYPEL .NE 
IF ( ITYPE .EQ. 
IF I ITYPE .GE. 
fiEWIND 13 
READ (13) IfiEAD 

I 
HEWIN_ 

IF (JTSafi -EQ. JSYES) GC TO 1575 



. 9 

3| 



A £ D ;;„ N £5„?. E 2- ° ) go to 2000 

GO TO 2000 
GO TO 2 100 



CF f IKEAC .EQ. 1 1 1 IH 
Cf i XSEAE .EQ. 12 ) IB 
JD IREAD 



BITE = 11 



* ead dc i§f| D I J = < 1 D iJi I) ' D1Y W' D 2Z(D» 1=1, SJT ) 

if ( BHI TbSWgo WUll * NSZZ(I) + NSXP(I > + "S"") 

BEAD (IHEAD ) jWBX (I , J» , U HTX (I, J) . SRI (I, J) ,SRTY(I,J) .HSZ(I.J) . 
3 ^2 Z ] I ^)/ t RXP(I,J^'&2TXP(i/ J ; # WEYP(f/j)',HET l YP(i:j) 

1565 CONTINUE ' 

COflHEST - INITIALISE BEVEBS AL ISDICATOES FOE JOINT CUEVES 
DO 1570 I = 1.HNJT 
DO 1570 N * 1)5 
,-_„ JCUHEV(I,N) = 

1570 CONTINUE 

GO TO 1590 
1575 CONTINUE 

H|AD (IHEAD) (DXX(I) ,DYY(I) ,DZZ (I) ,DVV(I) ,1=1. NJT) 
r .^,,.,S5AD IE£AD[ (GAMHS]l,J)\GA!!BTS(i',J) , J= 1 J3) , 1=1 , NJT) 
cnw^l I ^IP ALiSi BE¥E ESAL INDICATOHS'fOE JOINT'sHEAB STI 



COHHEN1 



1586 



CURVlsT " " -"—"""-"*»" *»*■ «vxn,i ^acna oTHESS-STB AIN 

DO 1586 I = 1,NJT 

JBV(I) =0 
CONTINUE 
DO 1587 I = 1,NJT 

IF ( gift :,J? X j<PS5«g<ftSf»»WM«CI)*MXfCI)*MW(TJ 

HEAD (IEEAD 

2 



1587 
COMMENT 



) ,.„ JWfiX (I, J) , «HTX(I,J) ,SRY(I,J) ,KRTY(I,J) .HEZfl.Jl . 

tUiJ i XNU iL 

Sn 1 ?!^ 1 ?* B I VE S? AL IHDICATOES FOB JOINT CUEVES 
DU nob X — 1 • HNJT 
DO 1588 N = 1,6 

= 



JCUEEV{I,N) 

1588 CONTINUE 

1590 CONTINUE 

EEiiIND N2 
BEHIND N4 

DO 1700 JJ = 1.NM 

ISTT = IST(JJ) 
IF { ISTT .EQ. ) GO TC 1700 
BODELT = aODEL(ISTT) 
A = HSTIF (ISTT) 
aP1= K+1 

hp2= a+2 

iEAD ( IHEAD ) ( DX(I), DY(I), DZ (I) . 1=1 
WEIi'E (N2) ( fiXJll- dHi) # V DZ(I , I '= 1,H 
IF ( INLOf(iSTT) .EQ. ) GC TO 1706 



1-1, a?2 ) 

•-P2 ) 



IKLOf(ISTT> .EC. 1 GC TO 170 

N2aAD = NSXL (ISTT) +NSYL (ISTT) +NSZL (ISTT) 



881^1 

00574 

00575*55 

00576 

00577 

00578 

00579 

00580 

00581 

00582 

00583 

00584 

00585 

00586 

00587*55 

00588 

00589 

00590 

00591 

00592 

00593 

00594 

00595 

00596 

00597 

00598 

00599 

00600 

00601*55 

00602 

00603 

00604 

00605 

00606 

00607 

00608 

00609 

00610 

00611 

00612 

00613 

00614 

00615 

00616 

00617 

00618 

00619*75 

00622 
00623 
00624 
,00625 
00626 
00627 
00628 
00629 
00630 
00631 
00632 
00633*75 
00634*75 
00635*75 
00636*84 
00637*80 
00638*80 
00639*80 
00640*80 
00641*80 
00642*84 
00643*84 
00644*84 
00645*84 
00646*84 
00647*84 
00648*84 
00649*84 
00650*84 
00651*84 
00652*84 
00653*84 
00654*75 
00655 
00656 
00657 
00658 
00659 
00660 
00661 
00662 
00663 
00664 
00665 
00666 
00667 



225 



2 white m) (( ; ; J ; ; R = U ; jAWjb I fa 

iOO CONTINUE " iliZfl < J " J > ' «STZH(I,J), J = T.10J, I = 2,KP1 f 00672 

IF ( HOB E IT .LE. -1 ) GC TO 1605 nnfi7u 

ELE«NT = ELEHN(ISTT) Snl4s*-»a 

IF (E Nl?NiE^ C 2 SHEAH) G ° T ° 16 ° 2 OOStI'tI 

.nnxtifaii << 00677*78 

00678 
) C0679 

00680 
) 00681 




REAB (IHEAD , (((EPBF1 h,J,K). f «FT1 jl. J, K I , SIBF1 jl.j,« , 88IIJ 

3 ISR 1 |H»«« SB*, ?•*•*- !»9"2& J.sJ J 00684 




3LBF1 fI,J,K}, 

KBITS (N2 ) (((EPBF1'(I;S;k h hhlm jU), SLBF1 (I J K) 00687 

^ SLSFT1 l'j,K) ; EPBF2 l!j'K ! EPBFT2 i'j K ' nnfiflZ 

GO TO 1603 1,HKPCS ), I - 2,HPl J 006 90 

1602 NHINGE=1 00691*78 

00692*78 
78 

78 
78 
78 
78 
78 
78 

1603" CONTINUE -*»»n*»«,»j, »-i, usual } , J= 1 , HNPCS) ,1=2, MP1) 00701*78 

HEAD (IEEAD ) ( ( (EPS MAX (I I J| , WSBIICI |,I J) ZPSP.RE (I,L, J) , 00703* 78 

white ( ,a ) ((£ |4« ji jgg, ; pi H fi , •.isSASju o° %°r 78 

*EAD (.HEAD ) <<(IGHOH (I, I.J, YTGEOW (I L, J, , J = 1,„ SPC S ,, 8o708 
2 «*IT B („ ) ((( J„o ' | *g |, 'r| G Io '( .^ a = 1#wcs J# 88709»78 
1605 CONTINUE 1,NhIhGE ), I - 2,MP1 ) °°711*78 

do 1610 n = i;3 8g7i§ 

1610 CONTINVE fiEV(I ' N) - ° 8M16 

55 l6^ D i EI = sjbr 1 » GC T0 170 ° Ml 

DO 1650 j " \'«Ul¥ 00722*78 

D0 lb =^ J ~ 1.HNPCS 00723 

1o50 CONTINUE 5 " ° 0724 

1700 fcRIT <yTINUi£ l( UT «» l « J »* J " 1,«KPCS) r L=1,Ni I INGE),I = 2,MP1 ) 00726*78 

2000 ""(^.gSM ) (( FCfi *<^>' I=1 '««>< J-1.6 ) 8SH 

IF TlTrPE .IE. 2) GC TO 5000 00730 

^100 CONTINUE On71l 

IF (JTSUB .ZQ. JSYES) GC TO 2200 0n7l?*fl9 

chHn°\tftn { Eh ' £0 ' "' si " 11 » X3 ' "» L5 ' DELWJT ) 00733*74 

2200 CONTINUE So7«*B'> 

C " L rfl - fl ,£IP JS « fiH ' a0 - B ' SL » 11. 13, 14, L6, DEIUJT ) 00736*82 

5000 CONTINUE "¥237*82 



ITYPEL - 1TYPS 0?3 I 



00740 



NITF = 
NIT EH F =i 
COHflENT - IEVRSE = 1 EEVEHSAL SENSEB 007U? 



IF I IEVES2 .EQ. ) GO TO 5105 

?n i„ A I?8I * £Q ' PfiI « T -OS- AP80B .EC MEKBEE ) GO TO 5103 



conazM* - = o not sensed 00743 

5100 CONTINUE 82 * = ° §g?«? 

00746 
00747 

5103 continue"" nn7uq 

PKINT 195 nnitn 

5105 CONTINUE 00751 

indL = - 1 o 00752 

gSSSISi : ITA?E = o 1 I^ E i H !ici s E 2 AfiE sgITcaED AS asoat §§2|1 

ITAPE = 1 nn7^A 

IF j IBTASE .NE.O ) ITAEE = 00757 

" ( ^APE .EQ. | GC TO 5200 00758 

P - St 00759 

N1 = NT 00760 

5200 CONTINUE gg 7 |1 

Ni - lN4 00763 



226 



N4 = N3 
S3 = NT 

NITF = NITF + 1 
NCHECK = 
BEHIND N1 
BEBIHD N2 
BEHIND S3 
REMIND N4 
COHBSNT 
COMMENT 

DO 5800 JJ = 1.NH 
ISTI = 1ST (J J) 
LTT — LT(JJl 
COMMENT - SKIP FOB NULL MEMBEB 

IF (ISTT .EQ. 0) GC TC 5750 



HATEIcIs B££ STIFFNESS "TRICES AND MEMBER FIXED-END-FOECE 



^P""ENT - SUBROUTINE FORKST CALCULATES MEMBEB (6 X 6) STIFFNESS HATHIX 

cgSJjjJii : smt™ k "° A ^ ANTAG£ CF sykeiey stoees ^compact vector BIX 
io po i £ i T i, { 2i a ' EC ' *' SL ' SHaT ' t1j L3 ' L4 ' L6 ' JJ * 

SHMT(I) 



55 00 CALL 

5510 
5700 



DO 55U 

sac { j j ,i) 

continue 

if ( xrvese .he. ) gc to 5705 

if (nitf .st. 1) go to 5750 

2MLD " 



rXSvPS ' IHSS2 0TIHE FOHHLD CALCULATES MEHBEB INCBEHENTAL FIXED-END- 
rR2S5S^ " ?S E SI„5 A 5?* X 0K FIEST IIESATION OF EACH PBCBLEH 
5705 " CONTINUE E&S 0CCUEEEE ' THEN *OBBlD IS ONCE AGAIN ACCESSED 

CALL DO 5710 f °I B = D l ( 6 SH ' fi °' "' SL ' r ° BT ' L1 ' U * l4 ' 16 ' JJ) 
5710 FOMM(JJ,l/ = FOMT(I) 

GO TO 5800 K ' 

COMMENT - S£T 5 |IXED i END-FORC£-HAIEIX TO NULL KATBIX FOE NULL LOADING 

5780 FOBB(JJ,I)' = 0.0 

3800 CONTINUE 
SEW 1KB N1 

BEHIND N3 nnahi 

COMMENT - DUMP OF STIFFNESS HATEIX AND LOAD VECTOE TO ACTIVATE qPT tic? Cinani 
C.B2ENT - FIVE COLUMNS IN PROBLEM NUBEEB CABD EQUAL TO PBINT ' LAST 0080 ? 
IF (APBOB . SE. PBINT) GC TG 77777 
DO 5900 JJ = 1,NK 
ISTT = 1ST (J J) 
LIT = Ll(JJ) 
IF <ISTT .20. 0) GC TC 5900 

CONTffiUE 3 ^^'^' I=1 ' 21) ' < ?0«»(JJ,D, 1=1,6 j 



mil 

00766 

00767 

00768 

00769 

00770 

00771 

00772 

00773 

00774 

00775 

00776 

00777 

00778 

00779 

00780 

00781 

00782*74 

00783 

00784 

00785 

00786 

00787 

00788 

00789 

00790 

00791 

00792*74 

00793 

00794 

00795 

00796 

00797 

00798 

00799 

00800 



5900 
77777 



COMHENT 
COMMENT 



COMHENT 
COMMENT 



PRINT 98 



JSYES) GC TO 16000 

ABE JOINT EQUILIBRIUM EQUATIONS 



CONTINUE 

IF (JTSHB .EQ 

START SOLUTION CF FB... 

SET CONTROL CONSTANTS FCB FEAME SOLUTION 

IHB = 3*IDJ + 2 

NL = 3*NJT 

HL = 1 

NFSUE = 21 
IF ( ITYPE .EQ. 2 
IF (NITF .GT. 



;pl 



) GO TO 6300 
GO TC 6300 



00803 
00804 
00805 
00806 
00807 
00808 
00809 
00810 
00811 

00812 

00813*80 

00814 

00815 

00816 

00817 

00818 

00819 

00820 

00821 



oT°a 2Sft£o5PfH§tf£S3 aNL£SS fl01DING FB0H A ™ I0DS ™*"4mi 



DO 6250 I = 1,NJT 
DXX(I) = 0.0 

,,„ DYY I = 0.0 

6250 DZZ(I) = 0.0 

0300 CONTINUE 

IF ( ITYPE .EQ. 
IF ( IE7ESE .EQ. 
COMMENT - DECREMENT JOINT DIS 
J = 
DO 6310 1=1, NJT 
J = J + 1 
DXX (1) = DXX (I) 
J = J + 1 
DYY(I) = DYY (I) •• CELHJT(J) 

DZZ (I) = DZZ (I) 

CONTINUE 
CONTINUE 

INDEX = 



6310 
6320 



1 .AND. NITF .EQ. 1 ) GO TO 6320 
1 ) GC TO 6320 
5PLACEHENTS 



EELHJT(J) 



DELHJT(J) 



00823 
00824 
00825 
00826 
00827 
00828 
00829 
00830 
00831 
00832 
00833 
00834 
00835 
00836 
00837 
00838 
00839 
00840 
00841 



C0.H3E.11 - 
COMHENT - 
CO HUE NT - 
COMMENT - 
COMMENT - 
CALL 



COMMENT 
6350 



"LL GBIP2A PCS SOLUTION OF FRAME JOINT EQUILIBRIUM EOUATICNS 00841 
GBIP2A SOLVES BOTH FRAME JOINT EQUILIBRIUM lODiflOSS AND OOfiUa 

||l|| |fIil s SI»l»!8I»I18f?x;,I ? Jiy# I >i IpSLIIi" 8818 
i, fftiSH^iMt tt-j-dii u - »• "• »■ ' pifr" 

ADD ON INCREMENTS CF JOINT DISPLACEMENTS 00851 

DO 6500 1 = 1- m-it 99852 



J = J + 1 



1, NJT 



DXX (I) = DXX (I) + HfJ) 

DELWJT ( J ) = H (J ) 

DYY(I) = DYY(I) + ill j) 

DELhJT ( J ) = H ( J ) 



00853 
00854 
00855 
00856 
00857 
00858 
00859 



227 



j + l 



65C0 



6510 



COMMENT 
COMMENT 



■"■*% 



DZZ (I) + 
J ) = 8 



DELWJ 
CONTINUE 

NITEEF = NITERF 

NCHECK = 

INDEX = 
IF (NITERF .NE. 

SCHICK = 1 

INDEX = 1 
CONTINUE 

IRVRSE = 

NMJ = 

KOFFJ = 
SOLVE FOR JOINT 



fJj 



( J 



2) GO 10 6510 



DO 6600 



I = 1 ,NJT 



REACTIONS 



OMMENT - SUBROUTINE INELST CALCULATES THE HESISTIVF SP55TT.T: unprp jkh 
OMMENT - THE SPRING STIFFNESS FOH THE JOINT SPRINGS FOLLOWING 
OMMENT - NONLINEAR LOADING , INELASTIC ONLOADING PATH 

INELST (I,SJX,SJY,SJZ,SJV,SJXY,QJX,QJY,QJZ,CJV) 
EQUILIBRIUM CALCULAflCNf If'eeVE^SALHAS BEEN W SEN 



CALL 



COMMENT - 



SKIP 

IF ( IRVRSE .NE. ) GO TO 6600 

Rxxm = - sxxtii+Dxxri) + 

RYY(IS = - SYY|l5*DYY{lj + 

gZZ I) = - SZZ|x)*DZZ(l + 

KOJJIJ = KOFFJ 
(IMJ(I) .EQ. 0) GO 

NflJ = NBJ + 1 

KOHJ (NHJ,NITF) = KCFFJ 
CONTINUE ' 

?J..i..5? v E§E .H|. ) GC TO 7300 



JSED. 



QJX 
QJY 
QJZ 



IF 



TO 6600 



ERRORS 
7250 I = 1.NJT 

EHXX(I) = QXX(I) 



660C 

COHHENT 
COMMENT 
COMMENT 
COMMENT 
DO 



-„BS ( 
7250 CONTINUE 

IF ( APEOB 
GO TO 7300 
7260 CONTINUE 

PRINT 155, NITF 
CONTINUE 



EXX(I) 




EQ. PRINT .OR. APSOE . EQ. HEBBER ) GO TO 7260 



7300 
COMMENT 



START NONLINEAR MEMBER SOLUTION 
IFAE — 
NMNC = 
DO 7500 JJ = 1,NM 
IMC(JJ) = 
NITM (JJ) = 
COMMENT - CALL SUBROUTINE MEMSOL FOR ITERATIVE SOLUTION CF MFKR^rc Tn 
COMmInI - SOLUTION B£& " END " FOECSS F ° E ™"" ECUI.IBEIUaCHicK a iN B FRAME 



CALL 



7500 

COMMENT 
COMMENT 



7650 
COMMENT 

7600 

COMMENT 
COME EN T 



„ , T * E ??OI. ( ,. 2M,EC,R,SL,L1, L3.LU, L6) 



Ii I 

SAVE 
FOR 



DO 
IF 



IRVRSE .EQ. ) GO TO 7600 

SONITOa D JOIKTS Sfl ° IS (CNLY) FEC " THIS FIBSI ITEBATI0N 
' N'SJ = 
7650 I = 1.NJT 
( IHJ (I) .EQ. ) GC TO 7650 
NMJ = NMJ + 1 
DXXMJfNMJ, 1 
DYYMJ(NHJ,1 
D2ZflJ(NMJ,1 
CONTINUE 

GO r TO N 5100 THB ADDITI0NAL F * AHE HE5ATI0N (REVERSAL CASE) 
CONTINUE 

iMlJISSSSI^ciSSSfStlSJS ^UILIBEIUM ERRORS FROM THIS 
DO 7700 I = 1,NJT 

"TO 7700 



= DXX(I) 
= DYY (I) 
= DZZ(I) 



IF 



(IMJ (I) 

NMJ = 



-EQ 
NMJ 



A 



GO 



7700 



8000 CONTINUE 



ERXXBJ (NBJ, NITF) 
ESYYKJ (NMJ, NITF) 
SRZZKJ (KHJ.NITF) 
DXXMJ(NMJ,NITF) = 
DYYHJ(NMJ,NITF) = 
DZZ M J (NMJ, NIT 
CONTINUE 



:tf = 



= EEXX 

= EKYY 
= ERZZ 

DXX 

EYY 

DZZ 



COMMENT - COMPUTE NUMBER CF JOINTS NOT CLOSED -- 
COMBENI - IBS TO SPECIFIED DISPLACEMENTS 
NJKC = 

DO 8700 I = 1,NJT 

IF(DABS (EEXX(I)) - GT. SEH1 . AND. D A3S (QXX (I) ) 

IFfDABS (ERYY(I)) . GT. ESR1 . AND. DABS (QY Y (I) ) 
2 GO TO dbOO ' 



00860 
00861 
00862 
00863 
00864 
00865 
00866 
00867*80 
00868*80 
00869*80 
00870*80 
00871 
00872 
00873 
00874 
00875 
00876 
00877 
00878 
00879*75 
00880 
00881 
00882 
00883 
00884 
00885 
00886 
00887 
00888 
00889 
00890 
00891 
CES ARE 00892 
ILIBRIUH 00893 
00894 
00895 
00896 
00897 
00898 
00899 
00900 
00901 
00902 
00903 
00904 
00905 
00906 
00907 

00908 
00909 
00910 
00911 
00912 
00913 
00914 
00915 
00916 
00917*74 
00918 
00919 
00920 
00921 
00922 
C0923 
00924 
00925 
00926 
00927 
00928 
00929 
00930 
00931 
00932 
00933 
00934 
00935 
00936 
00937 
00938 
00939 
00940 
00941 
00942 
00943 
00944 
00945 
00946 
00947 
SKIP CHECKS CORRESPOND00948 

00949 

00950 

00951 

1.0E+15) 00952 

„ „ 00953 

1.0E+15) 00954 

00955 



. LT. 
.LT. 



228 



2 IF(DABS < E£ ZZ($y 8& gS- EEB2 . AND. DABS (QZZ (I) ) .IT. 1.0E+15) 00956 

GO TO 3700 #0957 

§600 NJHC = NJNC + 1 noo! 8 , 

8700 CONTINUE 8x118 

nT . T „F (NJNC ,BQ. 0) GO TO 8900 881|S 

PEIJIT 175, NJNC.NITf nnolo 

IF ( NITF .fa. KNITF) GC TO 8950 nnqfiq 

IF JNHNC .ST. 0) GC TC 8950 nno^T, 

COHHEHT - HETdBH FOfi NEXT* FRAME ITERATION Bolts 

8900 CONTINUE 00966 

GO ^n A aqRn ,EQ - PEINT - CH ' APB0E ' E $- "BBSE ) GO TO 8920 00968 

8920 CONTIHUE 00969 

8950 ""UlLV*' ° 

couuit -Hiira^Sii cf rliiFilfiiiOfii NIIF IP 

HHJ = ° 0975 

KASTES = nnll% 

DO 8960 I = 1,NJT n%Vll 

IF (IHJ(I) .Eg! 0) GO TO 8960 nnVll 

NHJ = NHJ + 1 nnoZn 

DO 8955 J = I.SIIf 281§? 

„ P ' lIl, ? n J°^', I' J,DXX2J(HHJ,J) ,DYYHJ(NHJ,J) ,DZZflJ (NHJ. J) , 00983 

GO TO i9<N' J) ' EE * IIW <»k,J), £SZZKy(NHj7jr flJ " J '' 00984 

8952 "«& = 1 00985 



P^IST 183, I,J,DXXBJfNHJ,J» , D YYHJ (NHJ, J) , DZZHJ (NHJ, J) , 00987 

5 CoItiMI * ] ' ERYiHJ (« HJ ' J )' ERZZHj'(NBJ,J) 1 '' 00988 

CONTINUE 00989 

IF (KASTIR .EQ. 1) PRINT 184 aalll 

H jL^gOB .EQ. PRINT 'OH. APBOB .EC. HEHBER ) GO TO 8961 OOqq? 



GO TO 88961 U ' P ' T * 0H * RPB0B ' EQ ' HEMBEa > G0 T0 "61 00992 

S961 CONTINUE noaoo 

PE^Me 1 "" - E 2' 1 ) GO TO 88961 00995 

889b 1 ' CONTINUE 8R1I§ 

COEHENI - PRINT TABLE 8 IP REQUESTED nastl 

PEINI F l| IP8 * EQ * 1) G ° *° 897 ° 00999 

PRINT 16.NPEOB, (AK2 (II) ,11=1, 9) Oinni.cc 

IF (fijNC M. -Os! N«n£ ici. 0) PBINI 777 01002 

xaj.ni. ioi 01003 

RASTER = nmnii 

TEKPXX = 0.0 oifin^ 

TEHPYY = 0.0 oloal 

TEBPZZ = 0.0 01007 

DO 8966 I = 1,NJT oinnn 

onT „P,]KOJ(I) .EQ. 1) GO IC 8962 01009 

UJ,M GO T0'89*3 * (I> ' ° YY(I) ' °"W» RXKI), BYY(I), BZZ(I) 01010 

8962 KASTEfi = 1 PJgJJ 

8963 "^CONTINUE' °* X(I) ' DYY (I) ' DZZ <*> ' ax X(I), RYY(I), RZZ (I) 1013 

IF ( DAES(QXX(I)) ,G£. 1.0D+15 ) GO TO 8964 01015 

TEKPXX = TEMPXX + fiXX (I) 01016 

89t>4 CONTINUE l ' nini7 

IF ( DABS (fiXY(I)) -GE. 1.0D+15 ) GO TO 8965 01018 

oo-c IEKPYY = TEHPYY ♦ SYY(I) ' 01019 

89b5 CONTINUE v ; ninon 

IF ( DABS (QZZ (I)) .GE. 1. 00*15 ) GO TO 8966 01021 

.... „„„ TEBPZZ ■ TEHPZZ + BZZ(I) 01022 

39ob CONTINUE nin9i 

PRINT 157. TEKPXX, TEHPYY, TEBPZZ 01024 

8970 iiAikr* - eq - 1) s&Uj i5 « § || 

COBHENT - PBINI TABIE 9 IF EECUESTED 01077 

COaafST - EVEN tfaSN NOT REQUESTED, SUBROUTINE PEINT9 HOST STILL BE Q10?fi 

COHflENT - ACCESSED (10 TAKE CARE CF TYPE 9 PEOBLEH) . BUT DETAILED 010?q 

COMUBST - PHIiJTIHG CF HEHBER RESULTS SILL BE AVOIDED' DETAILED 01029 

KJ^WXND Ml nimi 

BESIND N2 niM-i 



NT = N1 
K1 = N2 
N2 = NT 



01032 
01033 
01034 



h z = h x n i m c 

COaflEBT - SUBROUTINE PEINT9 OUTPUTS MEHBEB RESULTS 01036 

8980 CONTINUE 81 "' 19 < AN2 • NPB0B ' *« ' *°. B » SI,L 1 , 13 , L4, L6) 01037*74 

COBHENI - PRINT TABIE 10 (JOINT ECUILIBRIUH ERRORS) IE REQUESTED 01039 

PRINT li ** Q ' 3 G ° TC § "° 010 "0 

PEiiiT 16,N?£OE, (AN2(II\ ,11 = 1,9) 010tt2*55 

filiXsi lit ' ' * SI# 0) PRIN,r 777 01043 

DO 8985 I = 1,NJT niouc 

898D PRIKT q 152, I § EHXX(I), ERYY(I), ERZZ(I) olottS 

160C0 CONTINUE 01048*7^ 

g§SSlS? : fSPSolS^ISIfH^fftg* JCINT e ^ilibrium equations miffil 

COBilENT - SET CCNIRCL CONSTANTS ECS FBAHE SCLUTION 01051*75 



229 



COMMENT - CALCULATE~THE NUMBER OF DEGEEES 01 FBEEDOH 
NL = 3*NJT 
QO 16 100 1=1, NJT 

16100 CONA| JST(IJ As ' °> » 1 ""*' 

HL = 1 

NFSUE = 23 
if LHP* s,BQ, 2 ) GC TO 16300 
It (NIxF .ST. 1) GO TO 16300 

COMEMI - Z£E<3 JOIHI DISPLACEMENT 
COaSSSl - OS A PHEVIOOS ITERATIOK 



UNLESS HOLDING FROM A EEEVICUS 



DO 



16250 
16300 



COMMENT - 



1.NJT 

■■ O.o 

; 0.0 

0.0 

■ 0.0 



.EQ, 

•EQ 



1 

. 
DIS 



AND. NITF .EQ. 1 ) GO TO 16320 

j GO TO 16320 

PLACEMENTS 



DO 



= 1 

+ 1 

1 



NJT 



16305 

16 310 

16320 

CCHdENT 
COMMENT 
COfldEHT 
COMMENT 

CALL 



16250 

DXX(I) 

Dtl (I) 

DZZ(I) 

DVV (IS 
CONTINUE 
IF ( ITYPE 
IF { IRVRSE 
DECREMENT JOINT 

J = 
16310 I 

J = J 

DXX (I) 

J = J 

on (i) 
j = j 

DZZ (I) 
(JST(I) 

DVV (I) 
TO 16310 

cohi8SS" , *" , ° vti1} " CELSJT < J > 

CONTINUE 

INDEX = 

g||f2S a Ig£{ a I Ioi8 1 ?liSISSiSi A ISu?ggL§8 S5I5J8S s Ji HS IlcIS 



IF 
GO 



DXX (I) - 

DYY(I) - 
1 

= DZZ (I) - 
ME, 0) GO 
= 0.0 



DELBJT(J) 

DELWJl(J) 

DELHJTjJ) 
TC 16305 



,„ EB » 
3000) 



80, I, 
GO TO 



SL. L3, 
16350 



COMMENT 
16350 



GRIP2A ( 
IF (IHE .IT. 10 
GO TO 9800 
ADD ON INCREMENTS OF JOINT DISPLACEMENTS 

DO 16500 1=1, NJT 
J = J + 1 



14, L6, IHB ) 



IF 



DXX (I) 

DELiiJT 
J = J 

dyy(ii 

DELHJT 
J = J 
DZZ (I) 
DELI.JT 
(JS 



16360 



16500 



16510 



GO TO 



ST (I) ,NE. 
DVVfll = 0.0 

16500 
J = J + 1 



= DXX (I) + 

♦v> -■ 

= DZZ (I) + 

.NE. 0) GO I 



J i J j 



(J) 



(J 



C 16360 



DVV (I) 
1 r i JT 



COMMENT - 

COMMENT - 
COMMENT - 
COEHEHT - 

CALL 
COMMENT 



DEL 

CONTINUE 

NITERF = 
liCHECK = 
INDEX = 

IF (NITEEF -NE. 
NCHECK = 1 
INDEX = 1 

CONTINUE 

IfiVRSE = 
NMJ = 
KGFFJ = 

SOLVE FOE JOINT 

DO 16600 I = 1 

SUBROUTINE 

THE SPRING 



DVV (I) + i(J) 
J ) - W ( J J 



NITEEF + 1 


2) GO TC 16510 



NONLINEAR LOADING 



REACTIONS 

NJT 
INELSI CALCULATES THE RESISTIVE SPRING FORCE AND 
STIFFNESS FOB THE JOINT SPRINGS FOLLOWING 



, INELASTIC UNLOADING PATH 



SKIP 
IF ( 



INEIST (I,SJX,SJY,SJZ,SJV,SJXY,QJX,QJY,CJZ.CJV1 
SeUILIflEldM CAldULAilCN^IF'BEVE^SAl'aAs'BEEN SEilSED. 




• NE. 



16600 

COMMENT 
C UK ME 1.1 



sxx 

SYY 

- SZZ 

- SVV 
KCFFJ 

IF (IMJ(I) .EQ. 0) GO 

i.MJ ■ KBJ + 1 

KOMJ (NKJ, NITF) = KCFFJ 
CONTINUE 
CALL SUBROUTINE 
JOINT 
DO 16700 I = 1,NJT 

SHHO (I) = 0-0 
IF (JSI(I) .EQ, 0) GO IC 16700 
CALL DJSTSK (I, STF J , SHMCJ ) 



16600 




16600 



DJS1SM TO OBTAIN THE SHEAR MOMENT AT EACH 



01054*75 
01055*75 
01056*75 
01057*75 
01058*75 
01059*75 
01060*75 
01061*75 
PROBLEM01062*75 
01063*75 
01064*75 
01065*75 
01066*75 
01067*75 
1068*75 
01069*75 
01070*75 
01071*75 
01072*75 
01073*75 
01074*75 
01075*75 
01076*75 
01077*75 
01078+75 
01079*75 
01080*75 
01081*75 
01082*75 
01083*75 
01084*75 
01085*75 
01086*75 
01087*75 
01088*75 
01089*75 
01090*75 
WHICH CALLS 01091*75 
01092*75 
01093*75 
01094*75 
01095*75 
01096*75 
01097*75 
01098*75 
01099*75 

01100*75 

01101*75 

01102*75 

01103*75 

01104*75 

01 105*75 

01106*75 

01 107*75 

01108*75 

01109*75 

01110*75 

01111*75 

01112*75 

01113*75 

01114*75 

01115*75 

01116*75 

01117*75 

01118*80 

01 119*80 

01120*80 

01121*80 

01122*75 

01 123*75 

01124*75 

01125*75 

01126*75 

01127*75 

01128*75 

01129*75 

01130*75 

01131*75 

1132*75 
01133*75 
01134*75 
01135*75 
01136*75 
01137*75 
01138*75 
01139*75 

01 140*75 
01141*75 
01142*80 
01143*80 
01 144*80 
01 145*80 
01 146*80 
01 147*80 



230 



idfij s !-sM TC 16700 my 



*? 



16700 CONTINUE 8iicn!ln 

IF ( ZR VESE ft E ) GO TO 17100 UM3U*oU 

IF(DABS(Qy/(I)) .GEV1.0E-H5T EBYY{I) =0.0 161*75 

ERZZ I) = QZZ (I) + SZZ(I) - SflHb{I) 01162*81 

IF DABS QZZ I)) .GE. 1.0E+15) EBZZ(I) = 0.0 OllfiT*^ 

lF (J iHJv\l>^0°0 G ° TC 170i> ° IttlUll 

GO TO 17250' ' 01165*75 

17000 CONTINUE BUIflBi 

EF.VV(I) = QVV(I) ♦ EVV(I) + SBKO (I) 011fifl*fiq 

17250 CO^Tliai ^ (I> } -Sfi- 1.0E*li) J EBVT(I, ^ 0. oTl69*75 

GO Jo A U300' EC * PHINT ,0B - APE0E * EQ - aSHBER J G0 TC 17260 01171*75 

17260 CONTINOE fUl 7 ,?!?! 

FEINT 155 NTTF 0(173*75 

17300 CONTINUE*" ^«W?3 

COMMENT - START NONLINEAR MEHBEE SOLOTICN 01176*75 

NMNC = 01177*75 

00 17500 JJ = 1,tffl ni17q*7l 

giaSi)"-^ oi 1 i^: 7 | 

COMMENT - CALL SUBROUTINE MEHSOI FOE ITERATIVE SOLUTTOM np wfwrttu to SiiIt^I 

SoSSISi : I^Sif5S BIfi - £ND ^ 0RC£S P0H j™* ico"BS° c N H^K s !il B FiAS E 8^If*if 

CALL .„ , T „^ i ? E£SCL ( £a,EC,B,SL,11,L3 € L4,L6) 01135*75 

175U0 dAiw ] - EQ - 1) ™ = ™ * ' ||:S 

r-rv- JC »», 11A 1ZVZSE • EQ. ) GO TO 17600 ni1fifl*75 

Rum - fsPaggfsSH^gfei""" (0NLI) F50H this fiest ite «^ion 8 |i:g 

ii'lJ = u 1 190*75 

DO 17650 I = 1.NJT 01 ?q?5is 

" ( W ( -Vmj Q ; 1 ) G ° T ° 1765 ° 01193*75 

DXXMJ(NKJ,1) = DXX(I) 01195*75 



DYYMJ(NMJ,1) = DYY(I) nil 

DZZBJ/NKjJl = DZZ I KU, 

176 50 rrvTT5n* BJ » NHJ ' 1 ' = DVV ^^ 01198*75 

Wb^J CONTINUE 01199*75 

COMMENT - EETUBN FOE THE ADDITIONAL FBA3E ITERATION (EEVEBSAL CASE) 01200*75 

oO TO 5100 Q1?ni*75 

17600 CONTINUE 01202*75 

NMJ = 01203*75 

CCflaSHT - SAVE JOINT DISPLACEMENTS AND EQUILIBEIDH EEEOBS FBCB THIS 01204*75 

COMMENT - ITERATION FOE MONITOR JCINTS 01205*75 

DO 17700 I = 1,NJT 01206*75 

IF (IMJ(I) .EQ. 0) GO TC 17700 01207*75 

HMJ = NMJ + 1 01208*75 

EEXXSJ(NMJ,NITF) = ESXX (I) 01209*75 

£HYYf!JiNKJ,HITF = EEYI I 01210*75 

EHZZKJ(NMJ,NITF = E3ZZ I) 01211*75 

ESVVKJ (NSJ,NITF) = ESVV(I) 01212*75 

DXXMJ(NMJ,NITF) = DXX(I) 01213*75 

DYYMJ JNSJ,NITF) = CYY(I) 01214*75 

DZZKJ(NMJ,NITF = CZZ(I) 01215*75 

,„„ A „ DVVMJ(KKJ,SITF) = EVV(I) 01216*75 

17700 CONTINUE 01217*75 

C02EEMT - COMPUTE NUMBEB CF JCIKIS NOT CLOSED SKIP CHECKS COBBESPCND01 21 8*75 

COMMENT - ING TO SPECIFIED DISPLACEMENTS 01219*75 

NJNC = 01220*75 

DO 18700 I = 1.NJT 01221*75 

IF(DABS (EEXX(I) ) . GT. EBB1 - AND. D ABS (QXX (I) ) .IT. 1.0E+15) 01222*75 

2 GO TO 18600 01223*75 

IF(DABS (EBYY(I)) .GT. EER1 . AND. DAES (QY Y (I) ) . LT. 1.0E+15) 01224*75 

2 GO TO 18600 01225*75 

IF(DAflS (EEZZ(IJ) .GT. EER2 . AND. DABS (QZZ (I) ) .LT. 1.0E+15) 01226*75 

2 GO TO 18600 01227*75 

IF(DA3S (£.KVV(I) ) .GT. EEE2 . AND. D ABS (QVV (I) ) .LT. 1.0E + 15) 01228*75 

2 GO TO 18600 01229*75 

GO TO 18700 01230*75 

18600 NJNC = NJNC + 1 1231*75 

1870C CONTINUE 01232*75 

IF (NJNC .EQ. 0) GO TO 18900 01233*75 

PRINT 175, NJSC,NITF 01234*75 

IF ( NIIF .EQ. KNITF) GC TO 18950 01235*75 

IF [NMNC .GT. 0) GC TC 10950 01236*75 

COMMENT - RETURN FOE NEXT FRAME ITERATION 01237*75 

GC TO 5100 01238*75 

18900 CONTINUE 01239*75 

IF i A ?S°E -**• PEINT -Cli. APEOB . EQ. MEMBER ) GO TO 18920 01240*75 

GO 10 18953 01241*75 

18920 CONTINUE 01242*75 

PHINT 177, NIIF 01243*75 



231 



18950 CONTINUE „.„, 

c 0UK » j Jix f JKrigj ^ ,SHP,jf2t»Bjij NITF lit! j:8 

NMJ = 01247*75 

KASTEB - SJISSrii 

DO 18960 I = 1,NJT ni^n* 7 ^ 

IF {l liH H fK 0) i go tc 13S6 ° oiili:?! 

59 !Sln._j".1?HI?* - 01253*75 

189 52 niofttt*4e 



^ IF <K0MJ(N3J J) .EQ. 1) GO TO 189 52 01?lttJ?i 

Efi"fl] sao" J i#««"<*aj#J) * ebyymj(nhj,o) , ebz£hj'(nmj,j) , 01256*75 

GO TO 1895* 

KASTEB = 1 
■ST 233, I, J,DXXEJ(NMJ, J) ,D ¥ YMJ {NBJ, J) .DZZflJfNMJ Jl 

rnKTTMMP ' 



01257*75 

18952 KASTEB = 1 01258*75 

ffai»T 2J3, I,J,DXXEJfNMJ,J),DS!YMJ(NBJ,J),DZZflJ<NHJ,J) . Olllo*?! 

18955 CONTINUE ' Sl 2 ,!?! 7 , 5 - 

18960 CONTINUE SJllllll 
IF (KASTEB .EQ. 1) PEIN1 184 Ollls*?! 
GO TO 88962* £Q * PB ° T * ° B * APB0B " EQ * « EHBE * ) GO TO 18961 01266*75 

18961 CONTINUE 8"2fZ!3f 

PBINT r i^6 IIYPE * EQ ' ' ) G ° T ° 88962 01269*11 

88962 CONTINUE %\V,^Zll 

CGXtfEltT - PRINT TABLE 8 IF REQUESTED fiii-rolni 

MlrfM"*' ' EQ - " G ° *° 1897 ° l\Wlt% 

PRINT 16 f NPBO£,(AN2(II) ,11=1,9) n1i?S2?l 

ESINT^Jtt C •"*■ ° - "* SH " C ' GT - °> PfiINT 777 01276*75 

KASTEB = 01277*75 

TEMPXX = 0,0 01278*75 

TEMPI! = 0*0 01279*75 

IEKPZZ — 0*0 01280*75 

TSMpvv = ft' n 01281*75 

DO 18967 I = lii J I 01232*75 

SHMCJ = -§aHO(I) ni?Ru*fln 

u , r , T |? i|OJ(D .SO. 1) GO TO 18962 01285*75 

2 IK SzZflf H#V?!?' I ilnS?li (1, *RSS^ I, ' DT7t «* "*<*>. "Y(I), 01286*75 

GO foMs96l } * SHHO(I), SHHOJ 01287*80 

18962 KASTEB = 1 V^lttk 

169o3 CONTINUE * * 

lRqu IF ( T D M^ x = ( iE«P G x E - + 1 ix^i) 5 > G0 T0 - 89M 7 7 

18964 CONTINUE AA l-W SHSsfJ"! 

IF ( IEififI ( IE«pff* + 1 B??tlf » G ° T ° 18965 l\l%%¥4 

18965 COHTXBSr" M BY * (I) 8«I2I?I 

1MM r iF ( %im^i\hii' .\iivj ■ G0 To ,8966 1 Is! 

18966 CONTINUE V ' ni^n?!?l 

If ( S52§^ VV (JU' GE - 1-0D+15 ) GO TO 18967 01302*75 

, 00 ._ TEMPVV = TEMP7V + BVV (I) HlinT*^ 

1d9t>7 CONTINUE ulJUJ*/3 

*K-fT 237. TEBPXX, TEHPYI. TEHPZZ,TEMPVV 01305*75 

18970 CONTINuI EB * E °* 1 » S&U * 15 « J SjjS 

COHJigfll - PRINT TABLE 9 If REQUESTED ailfl«i?i 

COMMENT - EVEN KHEN NOT BEQUESTED, SUBBOUTINE PHINT9 MUST qTTII HP niTnQ*4I 

3IHH : (SABS fi°.ISfl. c 5SI»fe s T iII L 'sS S S? • •»**'*"«•"• 

Ex-nlND HI Xl9l4i45 

S£WIND N2 KT . -- 01313*75 

HI = MS 01314*75 

82 = vt 01315*75 

COMMENT - SUBBOUTINE PBINT9 OUTPUTS MEMBER BESULTS 1317*75 

18980 CALL CONTINUE HINT9 < AH2 ' H ^0B,BB,B0,W.SL, I .1,L3,L4,Le) 01318*75 

COMMENT - PRINT TABLE 10 (JOINT EQUILIBRIUM EBBORS)IF REQUESTED 01 320 ^l 

PfilHT It ' 01321*75 

PRINT 16, NPBOB,(AN2(II) ,11=1,9) O1IIU7I 

PRINT 2J8 * G *° 2 ' SMK ^ • GT * 0) PHIHT 777 01324*75 

<onnc DO 18985 I = 1,NJT nilffl-?! 

'3990 CCNTiNUE 5 ' Z ' * &XX ™> SS"(I). EBZZ(I),EBVV(I) 01327*75 

COMMENT - RiT^N^O^N'EABc'lLEjr '"' °> G ° T ° 98 °° IM 

9000 GO TO 1010 4 330 

9800 CONTINUE ^ 

KLR = NIR + 1 SH« 

9805 llAtibl *"• SLEa ) G ° T ° la5 ° 

COa»EST s j j| SO^TXOH IS ABANDONED 01336*77 

9810 READ 12, NPROB.jAHWII) ,11 = 1,18) 0133^77 

IF (NPROB(f) ,$Q. IISSTl) GO TO 9900 01339*77 



232 



9900 CONTINUE 
HETOBN 
END 



rar 77 

01342 
01343 
01344 



REAL*8 HEHBER ' ' 



***** ****************** 



THAT DO 



EEAL*4 DISJT 
B£AL*4 FOHCEL, STEANL, 
] FORCER, STRANB, 

| FRMAXF, FRMAXD, 

i TOAXF, TOAXD, 

3 SHHJT 

B£AL*4 FOHTEB 
DIMENSION SMHT(21) 
DIMENSION F0HT(6) 
DIHEHSION FOETiH(50,6) 
DIMENSION TB(71) 



BHOBNE, 
FRHHCH, 
TOKOB, 



caavxi, 

CUBVAR, 
FEBBCT, 
TOBOT, 



SHFOBL, GAMBAL, 
SHFORE, GAHHAE, 
FBMSHF,FEHLTD, 
TOSHF, TCLTE, 



DIMENSION BH I6.L4), BO(L6) 
DIMENSION DELWJT (16) ' ' 
CCMKON /BX.OCK1/ X(251. 

2 QZZ(25), SXX(25), 

3 DYY (255. , 

4 SBXX(25), 

5 NSXX(25), 

6 NSYPJ25) , 
COKMON /BLOCK2/ 

2 DC2S{ 25) , 

J PEAGf25), 

4 lOP&Si 25), 

5 NALf 25 



4/ 



NAM 25), 
6 NSXj5( 25) 

COMMON /BLOCK 
2 JT1 (50) , 

COMMON /BLOCK7/ 



52 ( 22) , 
DY( 22) , 
SQX( 22), 
ST/ 22)',' 
BM1S( 22) , 

coaaoN /blocv 



DZZ 25? 
EEYY(25 
NSYY(25 
ISTJS (2 
DXS( 
PEF | 
EI. EH- , 
IFINL( 2 
NSXL ' 
NSY 
FOM 
JT2 a _ 
F( 22) 
QX( 22 
DZ ( 22 
SQY( 2 
u *( 22). 
BB2S( 22) 

ZMASSf 
-(2 



, H(L6) 

SYI(2$) , 
BXX/25J , 

EEZZ(25) , 
NSZZJ25), 






ZIS( 25) , 
QM{ 25), 



NSXP(2 



DCISf 25) , 
HH( 25)," 



INLOP( 25) , 
NAB( 25). 
IAXOPS( 25) 



5) , 

) .NFIXX 12 



tTS( 22f, 



NC51( 25 
NSZll 25 
NCDS( 25, . 
,131(50). IT (50), 

QZt 22 
EBY( 2. 
01 ( 22) , 
H2{ 22 ; 
AG( 22) 



2)" 




2 FTKJVV(25),TTBJ,^.>. 

COMMON /3Ldci&/ E1XXH JY5 t 2§} .EBXTHJ \%M)M 
I DXXMJ (5.25) ,DYYflJ (5,25) .6zZ«J (5.2 5) ,KOMJ 



FTMJXX (25) .FTMJYY (25),FTMJZZ (25). 
5) .NFTYYi25£,NFIZZ (25) ,NFT7 
ERZZKJ(5,25) , 



M 



FTVV(25) 



Uki.no t3,2i) ,DXYHJ (i>,25) .DZZBJ (5,25) ,KOMJ (5.25) . 
MMON /BLOC21/ ACCJTJl60) ,5ELJT(f06) ,ZBASSB 100) '.£ 
DVSIJT(100} ,FACCJTn00),FDAfiJT(1Q&) ,CDAM# 100) 
COHHON /BLdc22/_FJXTI25) .F&fT (25) ,^JZTV251 , FjIt (25)' 

DFJZT(25) ,DFJVT(25) 



DFJXT(25) .DFJYTjiS] 



..DACCJT(IOO) . 
i,DISJT(80,71) 

3) t 



1) ,NPBOB (2) 

SJST. KEEP3C,NCD3C, 



I 



2 DFJXI(25) .Duiiuaj .uruiii 1 

COMMON /BLOC23/ DFFS(4,25) 
CCMBON/BLOC24/ AN 1 (40 ) , AN2 (1 1 
COHHON /BLK1/ TOL, ELEMNl,NJST, KEEP3C, NCD3C, 

55SI1* KE|P3A,KEEP3E,KEEP4A,KEEP4B,KEEP4C,KEEP5A, 
KE2^5B,KEEP5C,KEEP5D,KEEE6, KE2P7, NCD2, NCD3A, 
NCD3a, NCD4A. NCD4B, NCE4C, NCD5A^ NCD5B. NCD5c| 
NCDSD, NCD6, NCD7, IP8, IP9, IP10, ITYPe' 
o ^? AN ' IFCRH, NH, NJT,' NSt! HIT, B. ' 

/ MP1. MP2, ISII, LTT, ITYPEL.IDj! NSTL 

2 cca '^Ui L Alis*lil^ 

COMMON /BLK5/ NFSOB.NITF, N 1 ,B2 

CCMMON / B ll 1/ / ^"^^^E.KSFFJ.KOFFQH.KOFFSE 
2 COSaON/ITC/ ^f^ E g|^ E El £ ES2,DII,CM,NTI,aH (20) ,MJ(20) ,BNITF, 
COKMON /HABN/ NJN^,N»N(5 



COKMON /NIT/' APEOB 

COKHCN /SKT2/ SEX (25. 10), 

2 WRV/25,10), WEXi(2B,lM, 

3 -«iETi(2S,1&) . BRTZ 25,10 ), 

4 HHTTP(25,lM 
'SKT3/ NCO 



BEY(25 

BBYP ' 
HSIV 



2 5.10), K 

[25, 1M, 8 

25,10 , U 



KBZ (25 
"BTi(23, 

BTXP(25 



1 10> • 

ETi(25 £ 10j, 

' r10) , 



COKMON /SKT3/ 
COMMON /SKT5/ 

COMMON /SKT6/ 
COMMON /SKT1 1/ 
COMMON /SKT13/ 



30NI, NITEBF 
KBXB (21,10) 
KRTXB (21^10) 



iBYM 



wsiinui.iui , x a 
NITEEM(50) , INDEX 
BSSINL, HSSIM1 

EP£1S(21,10,3) ,EPHT1S 
EPB2S{21,10,3 ,EPBT2S 



(21,10) , 
HETYH(21,10J , 



8EZH (21,10) 
»BTZB(21, 10) 



COiiJON /SKT14 / IBV (21,2,10) 
2 IBVESE, 

COMMON /SK1 15/ JJ 

COMMON /SKT17/ N4 

COMMON /SKT18/ NCHECK 

CCiJMON /SKI 19/ JCEGCN (25,6) , 

COMMON /SXT20/ BCEGCN?21,3 , 

COKMON /SKT21/ NTR, NTEA 

CUaflON /SKT22/ TIME. JT, IEEYN, 

COMMON /SKT26/ LTYPEL 

COaaON /SKT27/ IEEAE, IKEITE 



21,10,3 
21,10 ' 



ITAPE, 



JC0EEV(25,6) 
MC0EEV{21,3) 



IESTEP(71) 



FOB 
N3 



BOLD(50,6) , 



********** 
01345*74 
1346*90 
01347*90 
01348 
01349 
01350 
01351*82 
01352*82 
01353*88 
01354*88 
01355*88 
01356 
01357 
01358 
01359 

01360*85 

01361*74 

01362 

01363 

01364 

01365 

01366 

01367 

01368 

01369*42 

01370*42 

01371*42 

01372*42 

01373*42 

01374*42 

01375 

01376 

01377 

01378 

01379 

01380 

01381 

01382**5 

1383*82 

01384*82 

01385 

01386 

01387*85 

01388*88 

01389*82 

01390*82 

01391*82 

01392*56 

01393*79 

01394*61 

01395*61 

01396*61 

01397*61 

01398*61 

01399*61 

01400 

01401+79 

01402 

01403 

01404 

01405*88 

01406*88 

01407 

01408 

01409*84 

01410*84 

01411*84 

01412*84 

01413 

01414 

01415 

01416 

01417 

01418 

01419 

01420 

01421 

01422 

01423 

01424 

01425*84 

01426 

01427 

01428 

01429 

01430 



233 



f M 1ISlllII]IIllllIlil^ fill 



I mfflw*^™™wtiimmi: mm 

CC3H0N /SKT36V KSTIF<25> l"Tn*n/-?^i MrnuT/iev 01436*88 



3 SLBF2 

3 EPSMAX 



CgHMOH /f^T35/ fesTIF<25), E10AD(25>. BCDBLC25J. 01437* 88 

2 . 0. j, EPBFT1(21,tO,3), SLBF1 (21,10,3). 438 

2 ' 0'3 ' Ifl«2i : !l']H' **BFT2{ 2 1 10 3J 01439 
ii'i^fil' ->i-oelZ i 21 , 10,3 i , 01440 

5 Yg!o"}2 \'l- 10 ' YTGROK §H* 8 ' EPS?HE(21,2,10), 01441 

C0HHON /GI/ EJO 01444 

2 CO ^ELffll 8 0^^M^0 7 Hl, GABKAL(2D ' 71, ' SHFOEB « 20 ' 71 '' 8^31*88 

„ | A ? A SHK 4 5JKKi«"vmii.y gjgg 

11 FCBKAT ( 5H1 .BOX 10HT tdth i 01451*81 

12 FOBMAT (20 A 4) * ' THIfl ) 01452 

lynitf <m, qhi ai^'PF twi a-iw^'aw-iv/? sir* 

20 2? OHHAT(41fiD|N|aiC i SCLUlIo5 FAILED '^CONVERGE AFTER, 8J8lf 

Si J8IK? <^f"» 1UH "^ ^ P .I3,5X,7HTIBE = ,F10.4,//) S?Sfi 

SO^OEHAT ? fel| Efl0B fOLDHOS ABASDOHBD IN SEARCH OF AN INDEPENDENT 01461 

3 49E THE FOLLOWING CABDS HERE DISCARDED IN SEARCH, 01463 

92.MHBAT 1///,^ OYHAMIC SOIUTIOH FAILED AT TIHE STEP = ,15, \\\\\ 

94 FOMAI (/£ 48g glJASlciglDTlSi^^^gHIL, TRYING TO PROCEED, l\\\\ 

9S I F0 2 «AT C //* MK^-ffifSW" "" MWM»»//. Ijilj 

100 3 fSI h'dPEi4 ? 5) l1 ) 3, ' / ' "MM11.3)./. 6(1PE11.3, ) ffifi 

Jon IRISH ( 35 fl JOlk DISPLACEKENTS AT TIME = .F10.4 //) 0lu7fi 

120 FOadAT | 31H JOINT VELOCITIES AT TIM? = ¥ \o U /A S JiS 

130 FOSMAI f 31fl JOINT ACCLEBATIONS AT TIHE = jflolS;^ VSl 

155 roaiM (///3oa "i-Sj^aai^aMioj no .is.*. ***.*,/,, mil 

I Sf' 3o"i ,5?, T ITEB "I" iSfUU ROTATIONAL 014R 8 , 

ipus ^fse^smsk si: - III! 

207 FOBHM nx,16 B a E «BEE NUflkR = , I3,26H~HEHBEB BESPONSE AT THE , 0°!l8fcii 

210 FOBKAT (2GX,25H---- AT THE LEFT END ,\ 01505*88 

211 FOEi-iAT 20X'25H AT THE BIGHT FNn -ZZ'K] 01506*88 

2 12 FOBHAT {U ,'4H§IHE /l7H H Il|| GHT ||g E 'il.FORCE A^.DISPL 50°8*1I 

s;SH;ii fef ipwi»M|i 

M2 10MM (16H«gB fa BOgBHB - |Jg»j IfUsE OF THE SECTION , | ftf! 

»0 FOMM (IX, ^fXBi^fS "s.gj JIT AX. FORCE AX.STRAIN, 8 j HH 

i III if llii-ii 111^ 1i» 1 l c ;-r s Jff ^ 111 

25o FOSMAT Ju,t5HJOINT NOBBEfi'i ,13 ,28H-fiECOBDED DISPLACEHENTS- ) 0°1526*88 



234 



257 FOBilAT 
2bU lOBBAl 
777 FOEMAT 

2 

IF 
If 



2l3,F6.3,5MPE12.5n 
15H CHECK THE DATA) 

10H DATA**** j 30101 "^ DID SOT CLCSE - STUDY 
STEfl£ = Nil * SM 
APEGE . NE. PRINT ) GO TO 400 
GO TO 400 



MONITOH, 



NTEMF .LE. 30 ) 
PRINT = PENT NO 
FJBIHX 250 
400 CONTINUE 

TEMP = NTI 
TOTTKE = TEMP * DTI 
NTH ■ 
NJTT = 3*NJT 

DO 500 I = 1.NJI 
IF(ZBASS(I) .GE.O. 0) GC TO 410 
ZHASSR (3*1-2) =-ZMASS (I) 

zaASsah*i-ij=o.o 

ZHASSR(3*I)=0.0 

GO TO 500 



410 



500 



550 



ZMASS2 (3*1-2) = 
ZMASSR (3*1-1) = 



ZHASS(I) 
ZHASS(I) 





ZHASSS(3*I) = 
CONTINUE 
DO a50 I = 1,NJTT 

CDAME i I) =CM*ZMASSE (I) 
IF ^DABS(2MASSE(I)) .GE. 1.0E+15) CDAMP(I)=0.0 



.EQ. 4 ) GO TO 900 
1,KJTT 

.0 



CONTINUE 
IF (ITYPE , 
DC 6 00 I = i.«uj;i 
VELJT(I) = 0, 
6u0 CONTINUE 

TIHE =0.0 
CONTINUE 

DSS1 = 4.0/DTI 
DS52 = DSS1/DTI 
JLPIS If & CONTINUATION OF TYPE* 9 PROBLEM. THEN 
tiUST BE EIAD FECM ONIT «IBEAE« ' *" 

t. n *»*»m T l I IT *PEi- -EQ. 9 ) GC TO 940 
COaSfihl - IF THIS IS A NORMAL CONTINUATION OF TYPE 1 OR TYPP 
k COMMLNl - THEN UNIT 'IEEAD' IS NOT READ E 

IF ( ITYPEL -LE. 2 ) GC TO 1000 
" H THIS IS A NORMAL CONTINUATION OF TYPE 3 OE TYPE 
- THEN UNIT 'IBEAE' IS NOl EEAD 
If.JNIS «SQ, ) GO TO 1000 
CONTINUE 
REWIND 13 
BEAD (13) IfiEAD 

IF ( IEEAI .EQ. 11 ) IHEITE = 12 
IF I IEEAD .28. 12 ) IHEITE = 11 
COMMENT - HEAD OFF UNIT 'IEEAD" 
HEWIND IEEAD 

aEAD oi 942*1 = -f NJT (I) ' DYI(I) » D 22 ^ 1 )' I-1«MT ) 



900 



COMMENT 

coaaeiiT 



COMMENT 
COMMENT 

940 



VALUES 

2 PBOBLEM 

4 PBOBLEM 



NTEMF = NSXX(I) 
IF ( NTEME .EQ. 
EEAD (IEEAD ' 



NSYY(I) 
) GC TO 942 



) ?S1X(X,J),IETX(X,J) ,«RY(I,J) ,W3TYfI.J), 

i.ETi(i,j) wk£p(i,J) ,BBfxp(i,j) ,wEYP(i,5)',5 

J — 1,10 } 



♦ NSZZ(I) + NSXF(I) + NSYP(I) 

MHZ (I, J) , 
RTYP(I,Jj, 



945 
C0K3ES 
COMMEN 



950 



942 CONTINUE 

COMMENT - INITIALISE REVERSAL INDICATORS FOE JOINT CURVES 
DO 945 I = 1,MNJI 
DO 945 N = 1,5 

JCDREV(I,N) = 
CONTINUE 

IF THE LAST GOOD SOLUTION STORED ON UNIT 'IEEAD' H 
STATIC ANALYSIS THEN, VELOCITIES ETC. AEE NOT APPL 
IF ( ITYPEL .EQ. 9 .AND. ITYPE .EQ. 3 ) GO TO 950 
EEAD ( IEEAD ) JT, TIMS, ( VELJT(I). 1=1, NJTT ) 
H^AD | IEEAD ) ( ACC JI (I) , 1=1 , NJT1 / 

REWIND N2 
REWIND N4 

DO 980 JJ = 1.NM 

ISTT = 1ST (J J) 
IF ( ISTT .EQ. I GO TC 980 
M0D2LT = MCDEL(ISTT) 
ELEMNT = EIEMN(ISTT) 
SHINGE = 2 
M = MSTIF (ISTT) 
HP1= an 
MP2= K+2 
EEAD ( IEEAD j ( DX (I) , DY (I) , DZ(I), 1=1, MP2 ) 

S.EIIEJN2) i uiii), dj\1), mi). l*Y.nh | ' 

IF ( INLCEflSTT) .EQ. ) G<5 TO §80 

NBEAD = NSXL (ISTT) +NSYL(ISTT) +HSZL (ISTT) 
IF ( NHEAD .EQ. ) GC TO 952 
EEAD (IEEAD ) ( "- 

XEITE (N2) { ( H 

, 2 w 

952 CONTINUE 

IF ( MODELT .LE. -1 ) GC TO 954 

IF JELEMNT . EQ. SHEAS) GO TC 953 
.EEAD (IEEAD) ( ((EPE1S(I,J,K) , EEST1 S ( I, J, K) .EPF.2S (I,J, 
2 EPBT2S(I,J,K),K=1,2SSIH1), J=1,HNPCS), 



AS ENDING 
ICABLE 




K) * 

1=2, MP1 ) 



mm 

01529 

01530 

01531 

01532 

01533 

01534 

01535 

01536 

01537 

01538 

01539 

01540 

01541 

01542 

01543 

01544 

01545 

01546 

01547 

01548 

01549 

01550 

01551 

01552 

01553*87 

01554 

01555 

01556 

01557 

01558 

01559 

01560 

01561 

01562 

01563 

01564 

01565 

01566 

01567 

01568 

01569 

01570 

01571 

01572 

01573 

01574 

%\m 

01577 

01578 

01579 

01580 

01581 

01582 

01583 

01584 

01585 

01586 

01587 

01588 

01589 

01590 

01591 
IN01592 

01593 

01594 

01595 

01596 

01597 

01598 

01599 
01600 
01601 
01602 

01603 

01604*81 

01605*81 

01606 

01607 

01608 

01609 

01610 

01611 

01612 

01613 

01614 

01615 

01616 

01617 

01618 

01619 

01620*81 

01621 

01622 



235 



2 



WHITE (N2) (( ( gPElS 



a mn CM ) |(( W ?k J pI| Jl feW„ . sibf, L i,a,K 



iSHi 11:3:8; lilir&i f|: iSIWH'S- 
FS'Uhstf: WgiJi J f 8: B? J S «^T*' 



01630 
01631 



GO TO 95301 1,M*PC5 ), I - 2,A?\ j 01633 

953 CONTINUE RlllSffJ 

NHINGE = 1 01635*81 

READ (IfiEAD J ( ( (EPB1S (I, J K) , EPST1 SCI. J, K) „ 01637*81 

»» m ..< », •, N 1 ts^ ■«, £•»; ; : 

HEAD (IKEAD) CC<faU ti;3.ff,%I«ll J.» SLBF1 <I,J,K>. gf^I 

95301 CONTINUE »»rci (I, J, K) , K-1,BSSiai ) , J= 1 , HNPCS) ,I=2,HP1) 01645*81 

HEAD (IHEAD J ( ( (EPSMAZ (I I Jl EPSHIN (I L , J) , EPSPHE (I.L, J) , 01647* 81 

«hite c« ) ,« ps* s £ J: pI h i | |) '4?h f | i, 8iar 1 

\ F , IF f BODEIT .£.' iTlFlh'sh '•»»« f. I = 2,HP1 ) 01650*81 

nEAD ( i 2E AD , (((YGHOIf (I. I. J) . YTGBOB (I L , J, , J = ,, flHPCS ,, §]||] 

954 CONTINUE '» HIHI '* J " 2 ' HP1 J 01655*81 

DO 955 N = f*3 91||§ 

955 COWlSSS" 7 * 1 '"* =° 6 
958 li5I ^0 S TiNui {ECafiEV(I ' N) ' R=1 ' 3) ' I=2 ' BP1 » 3l|f| 

ii u c n T 2,ih - 1 ) Gc To 98 ° ojifi 

Eo° IfS $ Z hMV o l||*ei 

960 CONTINUE CI ' L ' J) = ° 01668 

iiRITE (H4) ((( IS?(I,1,J), J=1,HNPCS), L= 1 , NHINGE) , I-2.BP1 ) 01670*81 

980 CONTINUE oikti 

1000 CONTINUE P,l§7,1 

IF ( NTS .HE. ) GO TO 1020 0167} 

,--„ TOTTBE = TCTTHE + USE 01fi7a 

1020 CONTINUE nif-jS 

LTYPEL = IIYPEL 01fi7fi 

ITYPEL = ITYPE ni£-7T 



TIHE = TIHE - DTI 



t. u. J- m J- T U * U J. 

1046 CONTINU 



NITEHF = 1 



ITAPE = 1 



106: 



01677 



taban"- ii " Uii 01678 

NJNC =~0 ° 1679 

NTH = NTI ♦ 1 oifill 

_, n DO 1030 I = 1,NTI1 8JII4 

1030 5§STEg (X) = 8l f If 

1040 JT = JT ♦ 1 Rlf^ 

TIHE = TIHE+DTI Olfifift 

" i n A ?§SI ' EC - PEIH,r - CE - APB0B -EC KEHBEB ) GO TO 1044 01687 

1044 CONTINUE nififll 

IF (JT .EG. 1} PBINT 41 01690 



N.ITF = g || |2 



01694 



IBDIN = 5-igf 5 

,„r^ IHVESE= OlfiQfi 

1050 CONTINUE nifiQ7 

IF ( I3VBSE .EQ.O ) GC TO 1060 01698 

NT .OR. APfiOB .EC. HEBBEB \ GO TO 10<?5 OlfiQQ 



rn ^n*?n2^ - EQ - Palto * 0R ' APfi0B - EC > »EBBEB ) GO TO 1055 01699 

1055 CONTINUE S 22? 

PBINT 195 nilnl 

1060 CONTINUE 01703 



IF ( ISVBSE .BE. ) ITAPE - 01705 

c^ntinSe" - EQ ' ° ' G0 I0 107 ° Ml 



01707 



1070 CONTINUE NT g"10 

S£ - N3 0'712 

N3 : N^ §1713 

NITF_= Q NITF ♦ 1 01714 

KOFFJ = 9,U]§ 

NCHECK =0 01718 



236 



II j-SIll^K^Sc'iiss- ° » go io 11C ° ffiti 

XF Hckih v , eo ro 110 ° li*3 

INDEX = 1 1723*83 

1100 CONTINUE S???g* 83 

IHVBSE = 1/^3 

COMMENT - SOLVE FOR JOINT REACTIONS nVthn 
DO 1250 1=1 iJJT 

COMMENT - N0NLIN2AEL0ADING* INELASTIC UNLOaSiN^PA TE CII0BING %]]]°. 

IF (I N«iH N«S;i 0) G ° TC 125 ° 01738 

1250 CONTINUE < HBJ ' NITP > = KC " J i|3i 

1300 CONTINUE 01741 

td NITEEF = NITEEF + 1 ni7»l 

IF (IBVBSE ,NE. ) GC TO 1600 nil?.,. 

COMMENT - COMPOTE FOE EACH JOINT -THE SUB OF APPLIED JOINT LOAD ?! 

SI : ffiJWgbi'WII.>! IFliirM W«= 

DO 1500 I = 1,NJT SIJ8 

eexx(I) = cxxm + Hixm RUlS 



EBXX(I) = QXX(I) 
IF (DABSJQXX(I)f .dEl t.Ol+iS 



- -Elf f TIPS' form ;*EYi]i| EBix(I) = °'° g"|i 

IF (DABS^Yjdjf .flE l.oIJISJ EEXY(I) = 0.0 glMfJ 

ERZZjI) = QZZ(I) ♦ BZZ (I X S 

1500 SttgSi 8 *™' .•i. , 1.0l5!i) EEZZ(I) = 0.0 J ?P 

1600 CONTINUE PJ 7 ^ 6 , 

COMMENT - INITIALISI = THE N FOLLOHING VECTOES USED IN SUBROUTINE ADJTEB 01758 

EBXXDN(I)' = 0.0 rn^In 

BaiYDNJlj = 0.0 01760 

.... EEZZDN(I) = 0.0 S 15 

1650 CONTINUE PJ762 

REWIND N1 9,Xli}, 

5EBIND N2 9.XIH 

EESIND N3 PJ3§f 

SEHISD N4 ° 7 " 

GO iVmo * EQ " PEINT '° a ' iPE0B ' EQ - aEHBEB ) SO M 1700 <Ht68 

1700 CONTINUE 81411 

^_ PRINT 155, NIIF PJT™ 

1710 CONTINUE 01771 

TMESIP = ANOH n\nn\ 

NHNC = 5 21! 

DO 2000 JJ = 1,NH n\V,t 

ISTT = IST(JJ) ni-7-7T 

LIT = LT(JJ) PIT.?? 

IHC(JJ)=0 01778 

NITM (JJ) =0 ''" 

CCOHMEHT - SKIP FOB NOLL MESBEB SUi? 

„ IF (ISTT.EQ.O)GC TO 1850 S SI 

'-if jp^dsr- - fc "''-' "' " ' llnh 

C ?650 NX " Eo T 1900 B ! H = E 1 D 6 FOBCE "" AIBIX T ° N0LI SATBIX F0E SULL BEHBEE 01786 

19Q0 FORM(JJ,f) = 0.0 V.ffl 

19s0 CONTINUE QjZgg 

SSSSISS - ? p „P T I|Si L eS AS BEEN SE "SED 41 THE BEGINNING OF - 790 
rnZ%$& " A .» S H,-I X 8I STEP ' TEEN SKIP STIFFNESS FORMATION CALCOLATIONS 01791 

COMMENT - AT THIS TIME STEP SINCE WEONG INCREMENTS HAVFATRFTV rpfh ni-roo 
COMMENT - ADDED TO THE JCINT DISPLACEMENTS AT THE END CF TAST T?MF \tvv niio? 
COggEHT - SO EVEBYTBING MOST BE BACKED UP TO THE LAST TIME STEP C0B8?rrn 7M 
COMMENT - STIFFNESS MUST BE FORMED AT ITS END BFVTqpn TKrBtt*#f*<! 2nl E CI S S 

if N^flT.'^'/pEINT 7 T 7°7 200 ° Ml 
COflSlSi - SCLUTioN I ^N^ I ^r^ S 1 ^Fv B ISf°?icP' EN THE 1ASI G0 °0 STORED 800 

( IABAN*= Q i ° ) G ° TC 1955 01805 

PRINT 92, JT, TIME 01806 

go tE*M 7 * BQ - 1 ) GCTC 1110 ° "W 

1955 CONTINUE 1 809 

INDEX = 01810 

NC HECK = 1 

__..._ vm | F ( ISTT .EQ. ) GO TC 2000 Slil? 

CG4KEH - SUBROUTINE FOHHST CALCULATES MEMBER (6 X 6) STISFNESS MATEIX 0181« 



237 



S8MI : Mi^F-^ !? VAKTAGE 0f SIBMETEY STORES IN COMPACT 7ECT0H 
^ L DO 1960 F I B - 1 il BH ' BC ' B ' SL ' SB3T ' **» L3 ' ™« L6 ' ^ ) 

COHI§5§ ( JJ ;i) " »«W 

IF ( IfiVRSE -EC.. ) GC TO 2015 



1960 
2000 



COKHESt 
COKHENT 



fS&Hf&fllWJiiilSiF'' J0INT r »»cz««s. 



NIT? 

NITEBF 

IHDYN 

IBSIEP(JT) 

JT 

TIME 



1 
- 1 



DO 2005 I = 1,NJTI 



= NITF 

= NITERF 

= 1 

= 1 

= Jl - 1 

■ TIME - DTI 



2005 



2010 



VELJT(I)'= VELJT(I) - 
ACCJlflj = iCCJT(I) - 



DVEL JT m 



•A ■ I , fl JT 

(1) = DXX(I) - DELffJT(3*I - 2) 

(I = g||{| - DELS JT 3*1 - 1 

(I) = DZZ{I) - DELBJT (3*1) ' 



CONTINUE" " MCCJT 

DO 2010 I 
DXI 
DYY 
DZ2 
CONTINUE 
GO TO 10 50 
2015 CONTINUE 

H -L A £ EOt - HE - PAINT ) GO TO 2060 
DO 2050 JJ = 1,NH 
DO 2040 I = 1'6 

FOMTEH (JJ,I) =0.0 
CONTINUE 

ISTT = IST(JJ) 
IF (ISTT. EQ. 0) GC TO 2050 



2040 



2050 
2060 



2900 



3000 



PRINT 99~ ( S£c"(Jj;i) "l=l721l , 
CONTINUE *">li 

CONTINUE 

DO 3000 I = 1,NJT 
IF (NITF .ST. 1) GO TC 2900 
CALL DYSTLD ( FJX , FJY , FJZ,FJV ,TIJJE, I) 
FJXT (I) = FJX ' 

FJYI (I) ■ FJY 
FJZT (I) = FJZ 
CONTINUE 



( FCHTEK(JJ,I) , 1=1,6 ) 



EfiXX (I) = FJXT (I) 
ERYY(Ij = FJYT (I) 
ERZZfl) = FJZT (II 

CONTINUE 

NCHECK = 
INDEX = 

IF ( JT . GT. 1) 

IF ] ITYPE .EQ. 

DO 3140 I = 1,1 



ERXX 
EHYY 
ERZZ 



3020 
3040 



3060 
3080 



31G0 
3120 
3140 
32Uo 



3250 



3300 



3320 



3330 



3400 

CCK11ENT 

C 

C 



GO TO 320 
4 ) GO TO 3200 
uu Jitu i ■ 1 ,NJT 
IF ( ZKASSfi(3*I-2) .GT. 1.0C-10 ) 

ACCJ1 (3*1-2) =0.0 
GO TO 3040 

IF { 



GO TO 3020 



0.0 



ACCJ1 (3*1-2) = EBXX(I)/ZHASSB (3*1-2) 
fcSj?(illi"S , - , * t » 1-^-10 ) GO TO 3060 

GO TO 3080 

= EHYYJI)/ZHASSB(3*I-11 
.GT. 1.0D-10 ) GO TO 3100 

EEZZ (I)/ZKASSB(3*I) 



ACCJT (3*1-1) 
IF ( ZMASSE(3*I) 

ACCJT (3*1) = 
GO TO 3120 

ACCJT(3*I) = 
CONTINUE 
CONTINUE 
DO 3250 I=1,NJTT 



FACCJT (I)=ZMASSB(I)*ACCJT(I) 
FDA«JT(I ) =CDABP(lj*VELJT(l) 



CONTINUE 
DO 3300 1=1 

£B 
IF(DAES 



x-i ,NJT 

Es(rJXT(I) .GI. 1.00E*iO) EEXX(I) =0. 
EdYY I) = EKYY (I ) -FACCJT (3*1- 11 -PDAHJT ( 



F(DABS FJYi(I)) .GT. 1 .00E + 1 0) EB YY (I) = 
„ ,„ EoZZ (I) = EBZZ (I) -FACCJT (3*1) -FDAMJT ( 
FJDABSJFJZT(I)) .GT. 1 . OE+1 0) EEZZ (I) i 



IF (DABS ( 
CONTINUE 
DO 3400 I 



FACCJI (3*1-2) -FDAKJT (3*1-2) 

'(3*1-1) 
) = 0.0 
JT(3*I) 
0.6 



GO ]g A ^jg XX ( i ^' LT - 1 - 0E+15 - AN D.DABS(FJXT(I)).IT. 1.0E+10) 



ERXX (I) 
CONTINUE 



EEXXDN(I) 



GO io A 33i8 YY (I) ) " LT * 1 " ° £ * 15 * AHD - DAES ("*T(I) ) .IT. 1. OE+10) 

PP VV /Tl m TTDVTF(1lT/T\ 



,DABS(FJZT(I)) .IT. 1.0E+10) 



GO F ^ A ^ < Jg2Z(D).W-1.0E+15.AHD 

EflZZ(I) = ERZZBN(I) 
CONTINUE * ' 

IfiDYS = 1 DENOTES THAT THE PABTICULAE TIMF STFP apT»r, 
EXECUTED KOK HAS ALREADY BEEN COHPIETLY SOLVED CNCE BUT IS 
ACCESSED AGAIN THIS TIKE OKLY FOS THE PURPOSE OF 



81812 

01817*74 

01818 

01819 

01820 

01821 

01822 

01823 

01824 

01825 

01826 

01827 

01828 

01829 

01830 

01831 

01832 

01833 

01834 

01835 

01836 

01837 

01838 

01839 

01840 

01841 

01842 

01843 

01844 

01845 

01846 

01847 

01848 

01849 

01850 

01851 

01852 

01853 

01854 

01855*82 

01856 

01857 

01858 

01859 

01860 

01861 

01862 

81811 

01865 

01866 

01867 

01868 

01869 

01870 

01871 

01872 

01873 

01874 

01875 

01876 

01877 

01878 

01879 

01880 

01881 

01882 

01883 

01884 

01885 

01886 

01887 

01888 

01889 

01890 

01891 

01892 

01893 

01894 

01895 

01896 

01897 
01898 
01899 
01900 
01901 
01902 
01903 
01904 
01905 
01906 
01907 
01908 
01909 
01910 



238 

C (BACKED OP) STIFFNESS FCEHATICN 

2 Go" ^ A il|8"{ I JJ-«- 1 '"*".MD.DABS(PJIt(l)). 1 T.1.0S + 10) Sill] 

,..„ GO TO 3515 01915 

3510 CONTINUE 01916 

3515 ^4?^| {ESXX(I)) - GT - EEB1 > G0 *<> 5100 811H 

2 GO TC A 3li8 YY(in - LT ' KCE+15 - AND - DAES ( f ^m))-IT-1-0E + l0, 81118 

,-*„ GO TO 3525 01921 

3520 CONTINUE 01922 

3525 g M |t?S8I (, "" an ' GT - EBB1) G ° T0 510 ° JISH 

2 & T g A !fiS ZZ ( I ^-"- 1 -02 + 15.AND.DABS(FJZT(I)).IT.l.0 E+ lO) Stilt 

,.„ GO TO 3700 01927 

3530 CONTINUE 01928 

3700 Uul$&l laU{1 » - GT - EfiE2 > G0 T0 5100 SlllS 

COMHENI - PRINT TABLE 8 IF EEOUESTED 01931 

COUH, - g„ if >« !«&»! gfe fiES0LIS Fofi THE LAST „„ SIEp 01932 

IF IP8 .EC. 0) GO TO 3860 9 193 " 

PRINT 11 01937 

PHI NT 16, NPBCB, (AH2(II) ,11=1 .9) 193 8 

PRINT 18, JT.llSs l '' ' ' 01939*55 

EIINT 151 ' iJ -'^ 01940 

RASTER = PJ2 41 

TEHPXX = 0.0 01942 

TEHPXY = 0.0 SI?, 4 ? 

TEHPZZ = 0.0 19Ua 

DO 3850 I = 1, N JT 01945 

IF (SOJ(I) .EC. 1) GC TC 3800 01 9 i* 6 

3800 KASIEE = 1 01949 

3840 P:iI1, ?oNTi^£ J) " (1, ' D " (I, ' DZ2(I ),BXX(I,.HYT(I). B ZZ(I) Sllll 

2 ino A 3 S 8^ Z2(I)) ' GE - 1 - 0E+15 - °H.DAES(FJXT(I),.GE.1.0E + 10) 8lll| 

3842 COBIlSSI*" " TEHPXX + fiXX »> 81113 

2 £5 JgA{jfJpU».M.1.0«+15. OH.D*BS(FJIT(I,).GE.1.0E*10) Olll? 

3344 CO.TlSSI" 1 = TEHP " + ■»"> ojlff 

2 GO i§ A ||^ ZZ BJ).«B.t.0E + 15. OE.DABS<FJZT(I)).GE.1.0E-H0) 01961 

3850 CONTINUE ™ P " = TEBPZZ + EZZ < Z > ollll 

PRINT 157. IEKPXX, 1EHPYY, TEHPZZ nlffi* 

3360 coiiSai hsTEE - EC - 1 » P " NT 15 * J HI 

IF I JI .GT. 1 ) GO TC 3865 niqfifl 

PRINT F 9(! LTYPEL ' NE - 9 } G ° T ° 38b5 01969 

PEINT 120, TIHE nil?? 

PRINT 90°' ( ™ J *™> l = 1 ' NJTT ) 01972 

PRINT 130, TIfiE nlVil 

^ONtInUE ^^ I= '•»"> 0|?| 

REWIND N1 r>\Vi% 

BEHIND N2 g1"7 

8? : g^ ol"i 



3865 



N2 = NT 



01980 



3870 CONTINUE" " 01981 

RE«li D F l3 IA3AN ' EQ - ° J G ° M 339 ° HI 

!i.z , iJ 1 i.ift xu 

SEAD DC 3 l e8 E 4D I ) = < 1?L X T I) ' DYY(I »* D22(I) ' I=1 ' 8JT » g Iff 

IF | flfSB r4f 2 ? ( P G S fi^Iift * NSZZ ^ + «XP(I) ♦ NSIP(I) § 

READ (IREAD ) jSHX (I , J) . WRTX (I, J) ,MR Y (I, J) , HRTY (I J) WBZ (I Jl 01991 

3880 J CONTINUE ° " ''" ) g1§g| 

Htt HffiJ^flfcJiHf.WfS^f^'^J 81111 

Nil = NTH - 1 01997 

PRINT 96 l NTI1 1 01998 

iorn PRINI 18, JT, TIME Volll 

3890 CONTINUE ™ 

COKBENI - SUBROUTINE PRINT 9 OUTPUTS MEMBER RESUTS ninn-5 

,900 C *" c ™S^i Afi2 ' H " OB ' aH ' B0 '"' S1 ' L1 '"'»'") 0200°3 2 *74 

IF ( IABAN .NE. ) GO TC 3950 %?nni 

IF ( JT .EC. BUl'j GO TO 3910 02006 



239 



COHBEITj 
3910 

3940 
3950 



IF ( IP10 .20. 
- PBIHI TABLE TO 



) GO TC 3950 
- IF REQUESTED 

&Hjfi5; ,,/ " 10 '" ,fl - NE - «-»» 

PRINT 11 

IfzBZ lll N£,E ° B * <AH2 (XX) ,IX=1,9) 

DC 3 940 I = l.ffJT 
PRIST 152, I, ERXX(I) , 
PfiINT 90 l ' ' 

CONTINUE 

COMMENT - 5|g ( lgj-I8ip OT11 > G ° I0 1000 ° 
TI3E2 = TIHE + DTI 



GO TO 3950 



ESYY(I) , E2ZZ(I) 



DO 



If 



ix . ay 

( Ha, 



A NEB 



1 




1,NH 

1ST | 

LT | 
• ) 

se, 

EC, 
6 



3970 
4000 



4C50 
4 06 



4200 



4250 
4260 



IMES1P = 
REWIND N1 

NT = N3 
2J3 = N4 
H4 = Ml 
BEHIND S3 

I5AE 

NCHECK = 
INDEX = 
4000 JJ = 
ISTT 
LTT 
( ISTT . EQ 
CALL FOEMST 
CALL FOSHLD 

DO 3970 x = i,i 
FOHB (JJ,I) 
CONTINUE 
CONTINUE 

NT = N3 
N3 = N4 
N4 = NT 
IF i APRCE .NE. 
PBINI 98 

DO 4050 JJ = 1,KH 

ISTT = 1ST 
IF ( ISTT .EC. ) 
PRINT 99, ( SMC(J- 

CONTINUE 
PRINT 98 

CONTINUE 

DO 4200 I = 1,, 



JJ) 
JJ) 

GO TC 
W, St, 

V, SL, 



4000 

SHMT, 
FCH1, 



LI 
L1, 



13, 
13, 



14, 

14, 



L6, 

16, 



JJ 
JJ 



= FCHT(I) 



PRINT ) GO TC 4060 






TC 4050 
U21), ( 



F0BM(JJ,I) , 1=1,6 ) 



uu X = I , MOT 



IJYT fIJ 



FJZT. 



DFJYT(I) = PJY - 
DFJZl|l) = FJZ - 
CONTINUE 
JF (JT ,01. 1) GO TO 4260 
IF ,(NSflJ .EQ. 0) GO TC 4260 
DO 4250 II = 1,iiSHJ 
fiJOINT = MJ(II) 

3*11-2, JT 
3*11- 1,JT 
3*11 ,JT 



DISJT 
DISJ1 
CISJT 
CONTINUE 
CONTINUE 
DO 4270 I 
AA1 = 
AA2 = 
AA3 = 
VV4 = 
VV5 = 
VV6 



= DXX 

= Dir 

= DZZ 



BJOINT) 

HJOINT) 

JOINT) 



(a 



1,NJT 
ACCJT(3+I-2] 



1-2) 
±-1) 



3*_ 

3*1) 

3*1-2] 

3*1-1 

3*1) 



4270 



COMMENT 



ACCJ1 
ACCJT 

VE1JT 

VEIJ1 

VELJT 

ITE«p=3*I-2 

SIEfJhiiiI§ffi. 2 .JI5i5 p, * (2 - *" 1+¥Vft * BSS1 )* D ««(i) 

IT2flp=ITEHP+ 1 

"I! &$LiMtH*ffiM B) + (2.0*AA2 + VV5*DSS1) +DFJYT(I) 

IT£H£=I1EHP+1 
DFFS]3,I)=ZaASSai(ITEHP)*(2 

COKTIN^ Ail?(lkflP) * 2j * m 

IHB = 3*IDJ+2 

NL = 3*HJT 

ML = 1 

NFSUB = 21 
CALL GHIP2A (EH.HO, W, SI, L3, 14,16. IHE) 
IF ( IHB .LT. 16005 ) GC t6 4280 
SYMBOLICALLY MAKE NjilC = 1 

NJNC = 1 



.0*AA3+VV6*ESS1) +DFJZT (I) 



4280 

COBBENT 



4300 



PKINT 
GO TO 



IABAN = 

NTEHP = 
TEMP = 

94, NTEfl?, 

3870 



1 

JT + 

TIME 
TEMP 



DTI 



CONTINUE 

COMPUTE INC3EHENTS 

DO 43O0 I = 1,NJTT 

DVELJTfl) = -2.0*VELJT(I) + 

conti^^ CJtW = -2-0*accjt[i| - 



OF VELOCITY AND ACCEIEBATION 

2.0*H(I)/DTI 

4. 0*VELJT (I)/DTI 



+ DSS2*H (I) 



02009 

02010 

02011 

02012*55 

02013 

02014 

02015 

02016 

02017 

02018 

02019 

02020 

02021 

02022 

02023 

02024 

02025 

02026 

02027 

02028 

02029 

02030 

02031 

02032 

02033 

02034*74 

02035*74 

02036 

02 037 

02038 

02039 

02040 

02041 

02042 

02043 

02044 

02045 

02046 

02047 

02048 

02049 

02050 

02051 

02052 

02053*82 

02054 

02055 

02057 

02058 

02059*88 

02060*88 

02061 

02062 

02063 

02064 

02065 

02066 

02067 

02068 

02069 

02070 

02071 

02072 

02073 

02074*87 

02075*87 

02076*87 

02077*87 

02078*87 

02079*87 

02080*87 

02081*87 

02082*87 

02083 

02084 

02085 

02086 

02087 

02088*71 

02089 

02090 

02091 

02092 

02093 

02094 

02095 

02096 

02097 

02098 

02099 

02100 

02101 

02102 



240 



DO 4400 I = 1,NJTI 



4400 



4500 



(I) = VELJT (I) 
jlj = ACCJT(I) 
T(l) = 8(1) 



ACCJ1 

DELKJ 
CCNTINU2 
DO 4500 I = 

DXX (I 

DYY \l 

DZZ (I 
CONTINUE 
I? (NSMJ ,EQ, 0} GO TC 4610 
DO 4600 II = 1,1:SHJ 



DVELJT 
DACCJT 



|lj 



I = DXX(I) + H(3*I-2) 
ll) = CYY i) + » 3*1-1 
(I) = BZZ Ij * W 3*1) 



fij"} 



4600 
4610 

5100 



MJOIHI 
DISJI 

DISJT ( 3*II-i;jT+1 
DISJT j 3*11 JjT+1 
CONTINUE 
CONTINUE 
GO TC 10000 
CONTINUE 
IF (JT .NE 

IABAN = '1 
PRINT 92, JT, TIHE 
PRINT 260 
ri1 „ GO TO moo 

5110 CCKTINUE 

COMMENT - ITERATE MITHIN TIHE STEP 
COMMENT - ZERO DFFS - ONLY SOLVING 



MJ(II) 
3*11-2, JT+1 



1) GO TO 5110 



= DXX 

= DYY 
= DZZ 



HJOINT 
HJOINT 
HJOINT 



DO 



5150 



5155 



comment - 



51501 - ' F ° E EEB0B 

DFFS 
DFFS i 
DFFS 
CONTINUE 

DO 5155 JJ = 1,NK 
DO 5155 I = X'A 

FOMH (JJ,Ij = 
CONTINUE 

IHB = 3*IDJ+2 
NL = 3*NJT 
KL = 1 
NFSUB = 21 
CALL GHIP2A (fifl, 50, W, 3L, L3, L4,L6 , IHB) 
( IHB .Ll. 10000 ) GC TO 5160 
SOLICAILY HAKE NJNC 
NJNC = 1 



■ 1,NJT 
1,1) =0.0 
2,1) = 0.0 
3,1) = 0.0 



0.0 



IF 

SIBi 



1 



51oU 



5200 



5300 



0) GO 
1,NSHJ 



+ 
+ 
+ 

TC 



3*1-2) 
3*1-1) 



3*1) 

5410 



5400 
541C 

PR 

CJMEEtiT 



10000 



■ HJjII) 

3*11-2, JT 



10005 



10010 



IABAN = 1 
PRINT 92, JT, TIHE 

IF ( JT .EG.. 1 ) GO TO 11 100 

GO TO 3870 

CONTINUE 

DO 5200 I = 1,NJTT 

VELJ1 (I) = VELJT (I) + U 
ACCJT(I) = ACCJT(I) + W 
CONTINUE 
DO 5300 I = 1,NJT 

DXX (I) = DXX (I 
Dif Y (if = DYY (I 
DZZ (I) = DZZ (I 
CONTINUE 
IF (liSMJ .E 
DO 5400 II 
HJOINT 
DISJT 

DISJT ? 3*II-T,JT 
DISJT ( 3*11 ,JT 
CONTINUE 
CONTINUE 
IF ( NITF 
NT 20.MNI1F 
SYMBOLICALLY HAKE NJNC = 1 
NJNC = 1 
IABAN = 1 
PRINT 92, JT, TIHE 
IF { JT . £Q. 1 
GO 10 38 70 

CONTINUE 

IF { JT . LT. NTH 
A3TI1 = NTH 
IF ( AP20E .NE. SAVE ) GO 
WRITE (14,12) ( AN1(II), 11 = 1, 
CONTINUE 
IF (NSMM .EQ. 0) GC TO 10150 
DO 10100 II = 1,NSMH 
PRINT 205, HH (II) 

IF ( APROE .NE 
V.RITS (14,206) KM (II) 

CONTINUE 
PRINT 2 10 
PRINT 2 12 

TEMP = TIHE - ANTI1 * 
DO 10020 J = 1,STI1 

TEMP = TEMP + DTI 
PRINT 254, J,T£MP,FRMAX? (II,J) 
FRMRCT(II,J) 
IF ( APROE .82, S" ' 
WRITE (14,255) Hfl(II) 



(I)*2.0/DTI 
(I) *DSS2 



= DXX 
= DYY 
= DZZ 



HJOINT 
HJOINT 
HJOINT 



LT. KNITF ) GO TC 1065 



) GO TC 11100 



) GO TO 1040 



TC 
40 



10005 
) 



SAVE ) GO TO 1001 



ETI 



FRMAXD (II, J) 



,FRHHOH 
1LT 



F.CI II, J ,FRMSHF^II,J ,FEfl 
AVE 1 GC TC 10020 
,J,TEHP,FRMAXF(II,J) ,FRHAX 



H(H,J) 
Dill, J) 



urn 



D(II,J) 



02105 

02106 

02107 

02108 

02109 

02110 

02111 

02112 

02113*88 

02114*88 

02115 

02116 

02117 

02118 

02119 

02120 

02121 

02122 

02123*83 

02124*83 

02125*83 

02126*88 

02127*83 

02128*83 

02129 

02130 

02131 

02132 

02133 

02134 

02135 

02136 

02137 

02138 

02139 

02140 

02141 

02142 

02143 

02144*71 

02145 

02146 

02147 

02148 

02149 

02150 

mn 

02153 

02154 

02155 

02156 

02157 

02158 

02159 

02160 

02161 

02162*88 

02163*88 

02164 

02165 

02166 

02167 

02168 

02169 

02170 

02171 

02172 

02173 

02174 

02175 

02176 

02177 

02178 

02179 

02180 

02181+88 

02182*88 

02183*88 

02184*88 

02185*88 

02186*88 

02187*88 

02188*88 

02189*88 

02190*88 

02191*88 

02192*88 

02193*88 

02194*88 

02195*88 

02196*88 

02197*88 

02198*88 



241 



10020 2 CONTINUE ? EaK ° 3 (I1 ' J) ' * B32CT ("» J) ,fBKSHF (II, J) , FBBLTD (II 
PKINT 205. KK(II) 



.J} 



10022 



.IP ( APBOE .NE, SAVE ) GO 10 10022 
WHITE (14,207) AH (II) ' ^ 

PEINT 2 1 1 
PEINT 212 

TEH? = TIHB - ANTI1 * DTI 
DO 10024 J = 1,NTI1 

TEBP = TEBP * DTI 
2BIST 254, J,TEHP,TCAXF(II,J1 ,TCAXD (II, J) ,TOBOB (II. J) . 

-^«;#HiS«. , ifcaiB»Sf:ftb. B i. fl 



,-.,..2 ' 'TOEO 

3024 CONTINUE 

PBINT 220. HH(II) 



10030 



raiiii jL£\), nfl(II) 

IF ( APBOE .NE. SAVE ) 
WHITE (15,221) HH(II) ' 

CONTINUE 



GO TO 10030 



TEMP = TIME - ANII1 * DTI 

PHINT F 2il LEHl,(ISII) * E "' S ^ EAH) G0 T0 10060 
PBINT 230 

DO 10050 J = 1.HTI1 

T2HP ■ TEMP + DTI 
PRINT 254, J,TEfiP,FCBCEL{II,J),STRANL(II,J) , 
BBOHNLfll^jJ 'CUBVAL Il'j 
.APBOE .NE- SAVE ) GO fc 10050 



IF ( A 
B3ITE (T5, 



10050' 



-AVE I 
255) MB (II) ,J,TEHP,FOBCEL(II,J) , STBANL (II, J) 
BHOHNL II, J ;CDBVAL(II 



CI, J) 
CI, J) 



10052 



IT 220, Hfl(II) 

i*c sjasr aa (iif AVE » go tc ,o ° 52 



10054 
1C060 



10070 



CONTINUE 
PBINT 220, Hfl(II 

IF ( &-- 
■ BITE (15,_. 

CONTINUE 

FIIIX 252 ISaP = TIH£ " ANTI1 * DTI 
PEINT 230 

DO 10054 J = 1-8IH 

TEHP = TEKP + DTI 
PBINT 254, J,TEBP,FCBCEB(II,J),SIBANE(II,J) , 
1 t„ , ,„„„ = BBOMNB(II,J 'cUBVABfll^J 

• J -r^I P ,L A ?I9 B * SE - SAVE ) GO fc 10054 
rfAlTE (15,255) aa(II),J,TEaF,FCBCEB(II,J),STBANB(II,J), 

- bmohneIii.j Kcubvab ii.j 

continue 

GO TO 10100 

CONTINUE 
PEINT 251 
PEINT 253 

DO 10070 J = 1.NTI1 

TEHP = TEHP + DTI 
PEINT 254,J,TEaP,FOBCEL(II,J) .STBANL (II , J) , 

PEINT 220, KH(II) 



10072 



rii»i z/:u, nnij.ii 

IF I APBOE .NE. SAVE ) 
»BITE (15,222) nil (II) 

CONTINUE 



GO TO 10072 



1008.0 
10100 
10150 



TEKP = TIKE - ANTI1 * DTI 
PBINT 252 
PBINT 253 

DO 10080 J = 1.8TI1 

TEMP = TEBP + DTI 
PBINT 254, J.TEflp.FCBCEB (II, J) .STBANB (II.J) , 
2 aHOflNB(lf,Jl,CUEVAB(il,5);sHFOBB(il75r,GAHHAB(II,J) 

IF (APBGB -KB. SAVE) GO TO 10080 ' ' ' 

KBITE (15,255) KB (II) , J, TEKP, FOBCEB (II, J) .STBANB (II J) 

COHTlf5i I ' J) ' iDB7Xfl Ul.Ji ',SHFCBE(II,JJ I , GAbSaB (ii, jf 

CCNIINUE 

CONTINUE 
PBINT 11 
PBINT 110, TIKE 

PBINT 90°' ( EX2(I) ' B ™W' DZZ(I), 1=1, KJT ) 
PfiINT 120, TIME 

Hint 90°' ( VS1JT(I) • x = 1 ' NJ " > 

PHINT 130, TIHE 



PBINT 100, ( ACCJT (I) , I 

" 3J ,BQ. 0) GO TO 



IF (NS.1o 
DO 10250 II 



z -- ^m 



1 ,NSMJ 



1 , NJ TT ) 
11000 



113 

DO 10200 J = 1.NTI1 

IF ( II .Eg. 1) GO TO 10190 

IF MJO .15, 0) GO TO 1C190 

IF (HJO . ig. 1\ GO TO 10180 

IB (J) = DISJT(IIJ-2, J) 



DISJT (II3-5,J) 



mm® 

02201*88 
02202*88 
02203*88 

02204*88 

02205*88 

02206*88 

02207*88 

02208*88 

02209*88 

02210*88 

02211*88 

02212*88 

02213*88 

02214*88 

02215*88 

02216*88 

02217*88 

02218*88 

02219*88 

02220*88 

02221*88 

02222*88 

02223*88 

02224*88 

02225*88 

02226*88 

02227*88 

02228*88 

02229*88 

02230*88 

02231*88 

02232*88 

02233*88 

02234*88 

02235*88 

02236+88 

02237*88 

02238*88 

02239*88 

02240*88 

02241*88 

02242+88 

02243*88 

02244*88 

02245*88 

02246*88 

02247*88 

02248*88 

02249*88 

02250*88 

02251*88 

02252*88 

02253*88 

02254*88 

02255*88 

02256*88 

02257*88 

02258*88 

02259*88 

02260*88 

02261*88 

02262*88 

02263*88 

02264*88 

02265*88 

02266*88 

02267*88 

02268*88 

02269*88 

02270*88 

02271*88 

02272*88 

02273*88 

02274*88 

02275 

02276 

02277 

02278 

02279 

02280 

02281 

02282 

02283 

02284 

02285 

02286*88 

02287*88 

02288*88 

02289*88 

02290 

02291 

02292 

02293 

02294*88 



242 



10180 

10190 

10200 



10-280 

10290 
10300 



GO TO 1O200 

GO TO 10260 

TE (J) 
CONTINUE 
CALL CSPLOT (TK 
DO 10300 J 
IF ( II .£Q 
IF (MJO . EQ 
IF (flJO .EC. 



Tfi(J oo 



GO TO 103 
IE (J) 
GO TO 10300 

TEJJ) 
CONTINUE 
CALL CSPLOI (IB 
DO 10400 J 
IF ( II .E2 
IF (MJO . EQ 
IF (MJO . EQ 



DISJT(II3-2,J) -DISJT(1,J) 

= DISJT(II3-2,J) 

,1,1, TIKE, II) 
= 1.NTI1 

1) GO TO 10290 

0) GO TO 10290 

lj GO TO 10280 
= DISJI(II3-1,J) 



- DISJT(II3-4,J) 
-DISJT(2,J) 



10380 

10390 
10400 



10530 
10540 
10250 
1 1000 



TE (J) 
GO TO 10400 

TE (J) 
GO TO 10400 

TS(J) 
CONTINUE 
CALL CSPLOT (Tfi 

IF ( APSOB 
9HITE (16,256) 
TEMP = 
DO 10530 J 
TEHP = 
KEITE (16,257) 
2 DlijT(II3,J 

CONTINUE 
CONTINUE 
CONTINUE 
CONTINUE 



= DISJT(II3-1,J) 

= DISJT(II3-1,J) 

,2.1, TIME, II) 
= 1.NTI1 

lj GO TO 1C390 

0) GO TO 10390 

1J GO TO 10380 
= DISJT(II3,J) - DISJT(II3-3,J) 

= DISJT(II3,J) -DISJT(3,J) 

= DISJT(II3,J) 

,3,I,TIHE,II) 

•NE. SAVE ) GO TO 10540 



HJ(II) 
TIKE - AN1I1 * 



DTI 



1.NTI1 
IEHP ♦ DTI 
flJ(II) ,J,TEKP,DISJT(II3-2.J) , DISJT (II3-1 ,J) , 



11100 



IF ( IA3AN 
IF j IABAS 
IF ( NTS .£ 
DTI = D 
TEMP = 
NTI = 
ITYPE 
PHI NT 200 
GO TO 900 

CONTINUE 
EETUfiN 
END 



2. 1 ) HIE 

3. j GC 
.OH. NT 



-EQ. 
-EQ. 
Q. C . 
TI * 0.5 

( TOTTME 
TEHP 
= 4 



NTH + 1 
TO 11100 
IE .GT. NTHA ) 

TIME ) / DTI 



GO TO 11100 



92295 

02296*88 

02297 

02298*88 

02299 

02300 

02301 

02302 

02303 

02304 

02305*88 

02306 

02307*88 

02308 

02309*88 

02310 

02311 

02312 

02313 

02314 

02315 

02316*88 

02317 

02318*88 

02319 

02320*88 

02321 

02322 

02323*88 

02324*88 

02325*88 

02326*88 

02327*88 

02328*88 

02329*88 

02330*88 

02331*88 

02332 

02333 

02334 

02335 

02336 

02337 

02338 

02339 

02340 

02341 

02342 

Q23it3 

02344 
02345 



******** ********* **** ****** ******* 

SUBROUTINE JICOED 



SUBROUTINE ********************** 



rSSSlSI " SUBROUTINE JTCOED INPUTS JOINT GEOMETRY DATA (TABLE 2\ 

- CHECKS FOB BAD DATA. ,COBP0TES_jqi NT COORDINATES , ECHO PRINTS 



CGHttlfcl - DATA AND FEINTS COMPUTED JOINT COORDINATES 
IMPLICIT REAL*8 (A-H.O-Z) 
DIMENSION J2 (7 ' 

SXX(2 5) , 
DZZ(25), 
ERYY(25j , 
NSIY 25i. 
ISTJE (25[ 
TOL, ELEHBT,NJST, KEEF3C, NCD3C, 
ll^l 2 L g5FI A ' KEEP ^ B ' KBE?4 A,KEEP4B'KEEP4C,KE£P5A, 



COMMON /BLOCK 1/ 

2 QZZ(25) , 

3 DYY 2S[; 

4 ERXX(25J, 

5 NSXXJ25), 

6 NSYPJ25J, 
COM HON /BLK1/ 

2 
3 
4 
5 
6 



YY{2§) , 

XX(2S[ . 

ESZZ(25) , 

NSZZ(25 , 



Y 
S 
RXX 



QXX(25 
SZZ(25 
EYY (25 
QMJ (25 
IHJ 25 



QYY(25] 
DXX 25 
RZZ(25 
WMJ 25 

NSXP(2l 



if, 



MCD3B, NCD4A, NCD4B,'NCD4C; NCD5A; NCB5B, NCD5C; 
NCD5D, NCD6, NCD7, IP8, IP9, IP10, ITTPe! 

^OMMO^/BLK^MNJ-MNS^MNiT^ 



9 FOEMAT 

10 FOEMAT 

1 1 FORMAT 

I 

4 

12 FOEMAT 

13 FOEMAT 

14 FOEMAT 
2 

3 

4 10X, 

15 FORMAT ( 

16 FCEHAT ( 

17 FOEMAT 
2 

18 FOEMAT 

19 FOEMAT ( 
2 



lOX.IS^lffs^X.lE^^^IOX^E^^)" ^ 181 ° ATi ' ///J 
32H NUMBEE OF JOINTS IN FRAME =.15./. 

30" Y SffERENCI JOINT IS JOINT ,15. 'sa^AT 

5B X =,E12.3,10H AND Y = .BIO. 3,/ .IX. 

tK 25fi JOINT TOLERANCE IS ,£1013,//) 

10X,I5.5X,2E10.3,5X,7I5) ' r//) 

10X,l5,5X,2E11.i,5i,7l5) 
25X, 23H INPUT CF JOINT OFFSETS ,//, 
10X, 35H FROH X-OFFSET Y-OFFSET 

35H TO TC TO TO TO TO 
5HJOINT, 32X, 5HJOINT ,/) 
47X,7I5) ' 



TO 



,3X, 
,/, 



10X.I5) 
(48H 
158 THE 
( 338 
3(/) ,10X, 



FOLDING DATA FSOM THE PREVIOUS PROBLEM PLUS, 

FOLLOWING , //) 

NUMBER OF JOINTS IN FRAME = , 15,///) 

^I^S^H TED J0INT COORDINATES///, 10X, 
25faJOINT X Y ,/) 



*********** 
02346 
02347 
02348 
02349 
02350 
02351 
02352 
02353 
02354 
02355 
02356 
02357 
02358*79 
02359*61 
02360*61 
02361*61 
02362*61 
02363*61 
02364*61 
02365 
02366*79 
02367 
02368 
02369 
02370 
02371 
02372 
02373 
02374 
02375 
02376 
02377 
02378 
02379 
02380 
02381 
02382 
02383 
02384 
02385 



243 



11 MM | v>i*k.ntf.SF S0HBEfiS aDST BE P0SIT "* ) fl«gfi 

\\ 5§§gj¥ lis ^K N0RBEHS ' I5 - 12H not located > Silii 

SO^KMAT | III ^ ^JOINI j n& Lo« skllhl Kl^aliS* 1 » 

60 FOBHAT ( 43H NUMBER OF JOINTS IN FRAME GBEATF.B THAN, 02394 

in „ n r... , -!j? a - 3il -'BAt>i, ALLOWS) 0919=1 

TyOMM ( 35* iRi MM I MD T OFFSETS FOE JOINT, 17, 8]]}| 

80 FORMS ( 10B JOINT, 15, 30H HAS NOT PREVIOUSLY BEEN SPEC, 02398 

90 FOBHAT ( 32H EBBOE IN LOCATION OF JOINT , 15. 02400 

2 40H EXCEEDS THE TOLERANCE SPECIFIED ABOVE ,/.4X. 02401 

3 30H THE EEROB IN X DIRECTION IS 7 110,3, /.Vl. 02402 
PRINT 9 THE EHE0B 1N * DIBJ5CTIQH IS ,170.3)''' ' 02403 

'IF (NCD2 .EQ. 1) GO TO 8100 07U0R 

S(lc5S D ?«ij E o) S 6*ig-ii 5 s EBP2 - LE - ° » G0 T0 83o ° lm 

COBHENT - NO NEW DATA S 2 ^ , 7 , 

PBINT 17 R2408 

PHINT 23 22409 

GO TO 9800 07411 

1150 CONTINUE niaU 

JNTL = 07411 

IF (KEEP2 .EQ. 1) GO TO 1230 0741U 

COBHENT - ALL NEW DATA - SET COOHDINAIES EQOAL TO 1.01E50 02415 

X(I) = lJoiE20 niuXi 

1200 i\x\ = 1.01E20 HI}! 

COBHENT - EEAD FIRST CAED OF TABLE 2 n9uia 

HEAD 10,NJT,J1,DX,DY,TCL 07490 

PHINT 11,NJT,J1,'dX,DY;TOL 02U2 1 

IF (J1 .IE. 0) GO TO 8200 07499 

COBHENT - COMPUTE COORDINATES OF EEFEBENCE JOINT 02423 

IF (J1 .OX. NJT) GO TO 8500 02424 

i\ii\ = 52 02425 

GO TO Y i240 " DY 02426 

COBKENI - SOLOING DATA 07U9H 

C0 "?E N ?-,~ 2EAD FIESI CAED OF TABLE 2 02429 

1230 HEAD 16, NJT rsiHn 

PRINT 17 §3239 

PHINT 18, NJT 09UT9 

1240 CONTINUE 02433 

PHINT F l4" T * GT - BNJT) G ° TC 860 ° R2439 

N2M1 = NCD2 - 1 0243fi 

COBHENT - DO FOE SECOND AND SUCCEEDING CAHDS OF TABLE 2 02437 

DO 4900 JJ = 1,N2H1 0243A 

BEAD 12.J1.DX ,DY , ( J2 (II) ,11= 1 ,7) 02439 

IF ii L'%i i i- JT) jMlt " 1 02*40 

NJNZ = 0911111 

DO 1270 II = 1,7 §§2*2 

,„ n IF (J2(II) .ST. NJT) JSTL = 1 02443 

1270 IFjJ2|ll| .HE. 0) NJNZ =_NJNZ + 1 02444 

02445 



PBIiNT 13,J1,DX ,DX ,(J2 II .11=1, NJNZ) 

IF (J1 .IS. .OB. J2I1) .IE. 0) GO TO 8200 
cNT - CHECK IF FBOH JCINT HAS BEEN LOCATED 



J.x iu 1 .1.1,. u .OK. J^llJ .IE. U) GO TC 8200 02446 

COMMENT - CHECK IF FBOH JCINT HAS BEEN LOCATED 02447 

1300 IF X(J1) .ST. 1.0E20) GO TC 8800 02448 

If | M .15. 0.5 .Alb. DY .EQ. 0.0 ) GO TO 8700 02449 

Ir (JNTL ,hC, 1) GO TO 8500 07450 

COMMENT - DC FOR ALI JOINTS SPECIFIED CK THIS CARD 02451 

DO 4600 11= 1.8JNZ O2H2 

COMMENT - COMPUTE TEMPOEABY VALUES OF CCOEDINATES 02453 

3250 YT - vWl 1 ! t 81 02454 

« T ? *WU + DY 02I »55 

J2II = J2(II) 074S6 

IF M2II .LB. 0) GO TO 82C0 02457 

^ „ „„-, ? F U{J2II) .SI. 1.00E20) GO TO 4000 02458 

C"3S2hT - JOINT PREVIOUSLY LOCATED COMPUTE DIFFERENCE BETWEEN OLD 02459 

COBHENT - LOCATION AND NEB LOCATION EBX AND ERY 02460 

ESX = <X(J21I> - XI) 02461 

EBY = (Y(J2II) - YT) 02462 

IF (EBX .LT. 0.0 ) EBX = -EBX 02463 

IF (EEY .LT. 0.0 J EBY = -EBY 02464 

„„....,*„„ IF ( Eai - GT - TCL - ca - EB Y -GT. TCL) GO TO 8900 . 02465 

COMMENT - AVERAGE OLD AND NEW COORDINATES 074fifi 

X(J2II) = 0.5*(X(J2II) + XT) 02467 

GOTO 1 !^ - 8-S»lxtexi^ ♦ YlJ HI! 

COBHENT - JOINT NOT PBEVIOUSLY LOCATED 02470 

4000 X(J2II) = XT 02471 

Yfj2II) = YT 07479 

4500 CONTINUE_ ' 02473 

.,„„ 01— J 21 1 09U711 

4600 COSTIBUE 0747? 

4900 CONTINUE 0947fi 

GC TO 9800 09U77 

8100 PEINT 31 0947fi 

GO TO 9700 0947Q 

8200 PHINT 20 OTUflO 

GC TO 9700 02481 



244 



8300 PfiINT 30 n->.,o-. 

GO TO 9700 S32§3 

8500 PEINT 50 °24g3 

GO TO 9700 n^Zai. 

8600 FEINT 60 SiSfl 

„„ GO TO 9700 no»oT 

8700 PfiINT 70, J1 02487 

GO TO 9700 StmqS 

8800 PEINT 80.J1 Ytiial 

„_„ GO TO 9700 nouoS 

8900 PEINT 90 fi J2lI,MJf.ERI j&M 

98,0 &,iS.§!° 2IJII 

PfiINT 19 U2495 

COSKENT - PRINT JOINT COORDINATES AND CHECK FOE JOINT SOT SPECIFIED 02497 

9830 PRINTER (i^Y (I) ° E2 ° ' 0B - T(I) - GT - 1 - 0E2Q ) G0 T0 98 *° mU 

GO TO 5845 noini 

9840 PRINT 22,1 °2501 

nn r IABAN = 1 R?c.nl 

9845 CONTINUE n^nl 

9850 CONTINUE 92504 

9900 CONTINUE notnc 

BE1UHN XocSt 

END 02507 

fiMU 02508 



*****%ut%nf,lrlt*iVJX%**** : ******** SUBROUTINE ********************************* 

U "T — ^HRDnnTTKC M:3*Ti-f- TMnnmu r aaimvam « ■« »«.«..._ . . V42V ? 

>90 

fi"H" fl*7\ ~ "** ""*****" » *iuitvi*w^i l^wi w^j ij-'yO 

REAL*8 JTSHR.JSYES ' n °^]L„ 

DIMENSION J2( 10), JOINT (1<t) Q2?lg*II 

COMBOS /BL0CK1/ X{25) , Y (25) , QXX (25) 0YYf25) 07R17 

2 mm mm: nm\* HUE' iBSil: 

5 

6 , 

COMMON /BL0CK2/ DXS ( 25), DYS ( 25). ZLS ( 25). DC1Sf 25) 0?s5l*U9 

DC2S(25), PRf{ 25^ PRAE ( 25? . QfllW.' SlHS)!'' 02524*42 




SON /BL0CK1/ X{25) . 1(25), QXX (25) OYYf25) 09^17 

QZZ<25>, sixO|j t SYY(25), Szz 25 . fill fill ' olllfl 

*H*Sl: Jil5J.il/ Nszz|25 * ; ™ J < 25 f- ™?3ir. JIjjJ 



3 PRAG(25), ELEMN(25), 02525*42 

4 IOPOPl 25), IPINL( 25J, IPINR( 25), NC51{ 25), INLCP( 25). 02526*41 

5 NALi i|) ' HSXM 25), UXl< ( 25), HSZli 25 j J KlY 25) ? J ' 02527*42 
^->5, NSYRj 25), NSZR( 25). NCDS{ 25K IAX0PS ( $5) 

G^(25? < SJC'(25) 3S(25) ' HL ( ) ' HBJ ' 25) ' (25, ' T " J(2 - 

COaSON VSlQgftl/ pxi'f 25), DYL< 25), ZLL( 25), DCU( 25) t 02531 



6 NSXflf 2o5, NSYRj 25), NSZR( 25)' NCDS{ 25), IAXCPS ( $5) 02528*42 

COHHON _/BALa65/ JST(i5) ,§SsS(25) ,W(25) ,HHJ 125) ', VLJ (25) , VUJ (25) , 02529*79 

^ I HKJ (2D) ,GJ (25) ,SJC (25) 02530*80 

COHHON /BLOCR3/ DXlf 25), DYL{ 25), ZLL ( 25), DC1L( 25). 02531 

2 SgiWIll; IO Q 4 2 2 5 5f UQ ^ 25l; «0i(iif, IAXOPM25), o| 

^OMMOwkocW 5T°f(Po?^' SflC Ni Ta^o[f T ii B \50, ."SftfeO) 8IIIS 

COHHON /B1KV TOL, ' HjBMBl,SJSl/ K£if3C,HCD3fci l ' 02536*79 

2 KEEP2, KEEP3A,KEEP3B,KEEP4A,KEEP4B,KEEP4C,KEEP5A, 02537*61 

3 KEEP5E,K££P5C,KEEP5D, KEEP6, KEEP7 , NCD2, NCD3A, 02538*61 
| NCD3B, NCD4A, NCD4B, HCD4C, NCD5A, NCD5B, NCD5C^ 02539*61 

5 NCD5D, NCD6, NCD7, IP8, IP9, IP10, ITYPE^ 02540*61 

6 IABAN, IFORfc, NH, NJT, NST, NLT, H, 02541*61 

7 HP1 j. MP2, ISTT, LTT, ITYPEL,IDJ. NSTL 02542*61 
COMMON /BLKV MNJT, MNST.MNLT, HUH, BNC5 , MNC6, BDJl, HNJS,aNE,HNCS, 02543 

2 MNPCS,HNSS,aNQHM,HNJSI,MNJSS •>>••, 02544*79 

COMMON /SKT11/ MSSINL, BSSIH1 02545*79 

COHHON /CHAN1/ JTSHB 02546*62 

COSaON /CHAN13/ NPTJ{ 08), JSSjt 08), NTAO (08,08) , NGAM (08,08) , 02547*79 

2 NTAT(08), NGA1(08) ,TAaaLT(08) ,&ABHLT(0i) ' ' l °'»°>' 02548*79 

C03H0H /CHA31/ ALFHJ (8), BETJ (8), SBLSLJ (8) , GASTHD (8) , 0254 9*79 

.2 SL?BDJ(8i, TAOOLTJ8 . BATEJ (8) 02550*79 

o FOEMAT (5X. 3(15,1X1, 2X, 215) ' 02551 

7 FCHHAT (51, 3(15, 1X), 2x' 215, 3E1 1. 3) 02552 

3 FOEMAT ( ///,T0X, 40d COHPUTED HEMBEfl NU MBSSS .LENGTHS, AND OFF, 02553 

2 4BSETi,//,4bH MEMBEE FROM TO STIFF LOAD LEKGTH , 02554 

3 25H X-OFFSET Y-OFFSET ,/, 02555 

4 35H NOMB JOINT JOIHT TYPE TYPE,//) 02556 

10* fgftii K<6^ H I5, 5? B I L 5 E , 3C " 82HBEB L0CATION DATi ' ///} Ulir 9 

11 FORMAT ( 40H NUMBER OF BEBBEE STIFFNESS TYPES =,15,/, 02559 
2 5X, 35HNOMBEE OF BEMBEE LOAD TYPES =,15,///) 02560 

12 FOaBAT f 5X,I5,5X,2I5,5X,10I5) ' 02561 

13 FOEMAT 5X,I5,5X,2I5,5X,10I5 02562 

14 FOEMAT (25X, 26H INPUT OF MEMBER LOCATIONS ,//, 02563 

2 50B FROM STIFF LOAD TO TO TO TO ,02564 

3 30H TO TO '10 TO TC TO . /, 02565 
* 3oH JOINT TYPE TYPE JOINT,//) 02566 

17 FOR3AT (48H HOLDING DATA FROB THE PREVIOUS PBOBLEB PLUS, 02567 

2 15E THE FOLLOWING , //) 02568 

13 FOSHAT (//,47H *** COMPUTED MEBBER NUMBERS MAY NOT AGREE «ITH , 02569 

2 20H LAST PROBLEB *** ) 02570 

19 FORMAT (//,30a *** COMPUTED BEK3EB NOMEESS AGREE SITH LAST PROEL, 02571 

2 10HSM *** ) 02572 



245 



S3 fSlMt? f \U mlF) N ° aBEES mST BE ^SITIVE , 02573 

25 FOBflAT ( 32fl MEMBER WITH STIFFNESS TYPE ,15 9H AMD LOAD 02S7R 

I 5H TYPE,I5,/.32H HAS SPECIFIED 'Is' GOING PBO§J ' 02576 

3 7H JOINT ,15, 9fl TO JOINT, 15./, 17H PROGRAM ri^FS n?^77 

m 4 „„„ 36H N0T ALf.Oy THIS OBDEB TO BE BEVEBSED) ' n^7B 

y omi l iji of J0 ^!i T^r* cii ^ Sal « ™? §iiir 

6W0BMAI ( 51H ALlo ggHBEB OF STIFFNESS TYPES GBEATEE THAN STOHAGE, 02583 
62 2 FC£!IAT ( 46H ALL0 ™^Ea CF LOAD TYPES GBEATEB THAN STOBAGE, . 0258^ 
7WOEHAT ( 46B aaafl f|JFFNESS AND LOAD TYPES HOST BE POSITIVE, 02587 

72 FOEBAT { 51H STIFFNESS OB LOAD TYPE ABOVE GBEATEB THAN TOTAI n^fiq 
71 2 . ni} ,„ , 50H NOBBEH OF STIFFNESS OB iOAD TYPES SPECIFIED ABOVE)' 02590 

73 FOBflAT ( 51H YOO CANNCT HOLD DP THE LOAD BITHOOT SOME STIFF 02591 
-,, 2 5QHNESS - IF STIFF TYPE = - LOAD TYPP Nfl£*- _ n ,'noSoo 

74 FOBHAX ( 45H HAXIHUM BAND WIDTH OF EQUATIONS EXCEEDED / ' 02593 

91 Wi H gggg B I2 J ?Js"S!s IoI B gI h¥ §! § ISDtIW 

I 49H DO HOT AGBEE BITH PREVIOUSLY DEFINED OFFSETS 02598 

5 46B FOB A SEflBEB OF THIS TYPE, WITHIN THE ALLOWED / ' 02599 

7 IBS) EBR0E ° f T8 ° IIMES TEE JOIHT I0CATICN T0L§SisC, 02600 

92 FOHHAT ( «5| EBfiOfl IN OFFSETS FOB HEHBEB OF LOAD TYPE, 02602 
3 I ^ A4 |I JOI.ilflS/SB LraBJ™" THE HEBBEE BETBE ^' §1111 

| fob J° g g«B AG SPtg!l B ,?fs: i SSISL D !II»IE 1 g5li5!' § 

7 1BE) TIHES THE J0IKT L0CAT I°N T0LEBANC, 02607 

93 FOBflAT ( 51H NaflBEB CF JOINT STIFFNESS TYPES HOST BE POSITT 02609*62 
,/„.,„,„ , fOBVE AND LESS THAN OB ECOAL TO THE ALLOWABLE STOBAGE) 02610*62 

94 ForiHAT ( 51 fi JOINT STIFFNESS TYPE SUST BE POSITIVE AND LESS 02611*62 
qc; 2 *,--*^ i tfS THaN ,9? E °- UiL T0 IHB NUHBEE CF JOINT STIFF TYPES I 02612*62 
9d Fiju.IAT ( 46H ALL THE JOINT STIFF. TYPES ABE NOT nFFTN^nf ' n?fiiT**o 

96 FOEMAT \ 50 fl OBIENTATION OF AHORIZONTAL BEflBEB D HAS K TO ) BE , 026 6 14*77 
Q1 2 . r ,„. , ?§1 IN TH £ POSITIVE X-DIRECTION FOR THE JSYES OPTION) 02615*77 

97 FORMAT ( 50H OBIENTATION OF A VERTICAL HEHEEB HAS TO BE IN 02616*77 
9a 2 FCBHAT I \\l IHE ggSIIIVE Y-DISECIIOK FOB THE JSYES OPTION) * ' 026 7*77 
98 2 fCBBAT ( 51H JS „§» jJjfgg'AWniAl FBAflES CAN BE ANALYZED IN THE. 026 18*77 

99 FORMAT ( 46H EBBCB IS THE HESBEB BITH STIFFNESS TYPE =, 15, 02620*77 

1 1 !h lO^JOTNI T lIF = ' I5 ' 20H THAT CONNECTS JOINT, 15, 02621*77 

I! Li i v |p B " «iw?3P~ iiiif.r— | 

lift fCBHAT I5,5X,'6e1o.3,I5) n 2 fi 2 q*7 2 

IH FOUlt I/AJJJ y J INT STIFF HLJ HEJ VLJ , 

3 9n tvdf /i ■""»" u»j i<J" #/, 02631*79 

116 FCBHAT (5X,I5°5X,6Eli:!;ii, Sll^!?! 

hi bhh h-si agfcB™ nirrfeMisn;' ■•«■«•■■•"» I ; 

,-,* , „ . 34H BIAL NUMB PTS OPT = NO) ) n?617*7q 

i in msm^^^^r> i 

2 Zt ill C HvI I N T „ fi „ E B B El a I^u!g D B D E LD Ip^!!lD A \ STBESS - STEAIN ' J 

151 rOEflAT ( 47H BOTH SBEAE aoEOLDS AND SHEAR STEESS-STflAIN, 02644*79 

^ 5 H H §s%gSPif>! i f l0X BE 3PECIFIED F0E A J0lfT - t: 

152 FCBKAT { 50K JOINT SHEAR STRESS-STRAIN CUEVE NDHBEB SHOOLD 0?fiU7*7q 

i53 3 fo 2 «at , II fflxffiifiMS.HreSSM ffi.jfti'raMKR ' : 

5 2 FO T lit ^I^ 3HE AB B DS S PTI^ !I U^Foill T 31111 f B " HEN ' ** 

154 2 FOBBAT ( 49H ^g™ IS NOT EQ0AL §0 1, NCD 3 I IaS TO BE, 8|||J ; J| 

ill ln S M A ? I S?l MJHBER OF CAEDS IN THIS TABLE HOST BE EVEN) 02654*79 

OFO.BAT I 4 7H IF S „„p j GP,IO.-1 , FIRST POINT ON cSSIIl 8||||*|| 

I 1 12 £9fSiS I ft2? SYBHE?BY OPTION'HUST BE 1 OR ) 02657*79 

158 2 ?CEMAT I 48H ^ NUHBEE CF POINTS ON COEVE MOST BE bWbEEN 2, 02658*79 

159 FOBflAT ( 50H TOO LARGE A NDHBEB FOB STRESS-STEAIN CTJKVE NU 02660*79 

l«lrt 2 D/^„, w - 35HBBEB OB NO COEVE NUHBER SPECIFIED ) ' 02661*7q 

iti ioii^i ( H i§ a Mf: s IlAi! B c i EV iIpgT H i B l E fIIt 18SS5 B'SP 

D i il K ^f E f^Ij s s-f?I / AIN CBfiVE IS SP£C "^« "."SI S8ii?s, 8||i|:|8 

DATA 1TNC /4H / nlffli§8 

COMKEHI - INPUT TABLE 3A n?ccT*Z? 

PBINT 100 02667*62 

J 02668*62 



246 



pEIH P 1( ^TSHfi.EQ.JSl£2S) GO TO 210 



COMMENT 
210 



GO TO 510 

SET ALL THE JOINT STIFFNESS TYPES TO ZERO 

IF (KEEP3A .BE. 1) GO 1C 215 
T 17 

50 TO 215 



«CD3A .HE. 0) 



215 
220 



PRINT 

IF (NC! 
PHI NT 2 3 

GO TO 510 

JKTL = 
DO 220 J = 1,NJT 
JST(J) = -1 
HEAD 110,NJSI 
PRINT 111.NJST 
r^u,-™ IF(NJST.LE. O.OR.NJST.GT.MNJST) GO TO 8930 
C0H8EKT - READ JOINTS HITH THE SAME TYPE NUMBER- 
PRINT 1 \z 

NTEHf = NCB3A-NJST-1 
DO 400 J = 1, NTEMP 
READ 110, JSTT, (JOINT (II), 11=1, 14) 
NJNZ=0 
DO 250 II = 1,14 
IF (JOINT (III .GI.NJ1) JHTL=1 
IF JJCINT(II).NE. 0) k 
250 CONTINUE 

COMMENT-PRINT JOINTS HITH THE SAME STIFFNESS TYPE NUMBER 



NE. 0) NJNZ = NJNZ + 1 



PfilNTJ 13 f JSTT, (JOINT(II) .11=1, NJNZ)' 



COMMENT 
COHKENT 



300 

400 
COMMENT 



»i i u.djii, (iJUXNT (1J.J ,1J.= 1,NJNZ 
IF JNTL.EQ.1) GO TC 6500 
IF JJSTT.LT.O.OH. JS1T.GI.NJST) < 
ASSIGN JOINT STIFFNESS TYPE NOB) 



410 



...... GO TO 8940 

ON ONE CARD 1 STIFFNESS ITPE NtJBBEE FOR THE JOINTS SPECIFIED 
DO 300 K = 1,NJNZ 

KTEMP = JOINT (K) 

JST(KTESP) = JSTT 
CONTINUE 
CONTINUE 
CHECK WHETHER AIL THE JOINT STIFFNESS TYPES ARE DEFINED 

DO 4 10 J = 1,NJT 

CONflN-oV" 35 ^-* -- 1 * G ° T ° 895 ° 
PRINT 115 

DO 500 J = 1.NJST 

print }lc'™ll'$™'%l%hlH£*lMl'lMihi31'$c 

IF 



116,JSTT,HLJT,HRJT,7LJT,VUJT,THKJT^GJT^NC 

(JSTT .20. 0) GO TO 500 

HLJ(JSTT) = HLJT 

HRJ(JSTT) = HHJI 

VLJ(JSTT) = VLJT 
VUJtJoTT) = VUJI 
THKJ(JSTT) = THKJT 
GJ(JSTT) = GJT 
NJSS(JSTT) = NC 
COMMENT - COMPUTE THE JOINT CONSTANT THAT IS USED TO CALCULATE JOINT 
COMMENT - SHEAR MOMENT AND JOINT STIFFNESS. 

SJC (JSTT) = THKJT* (HLJT+HRJT) * (VLJT + VUJT) 
IF (GJT .20, .AND. NC . EQ. 0) GO TO 9150 
IF (GJT .ME. .AND. NC .Ml. OJ GO TO 9151 
IF {NC .LT. .OR. NC .ST. MNJ5S) GO TO 9152 
CONTINUE 
INPUT TABLE 3D 
51U PRINT 120 

IF (JTSH2 .20. JSYES) GO TO 520 
IF (NCD3B -MB. 0) GO TO 9153 
PRINT 101 

GO TO 1090 
CONTINUE 

NTEMP = 
DO 521 J = 1,NJT 

JSTT = JST(J) 

NTEMP = NTEMP ♦ NJES (JSTT) 
CONTINUE 

GO TO 522 
GO TO 9161 



5U0 
COMMENT 



520 



521 



, HE. C) 
. NE. 0) 



522 



525 



530 
535 



, NE. 1) GO TC 525 



COMMENT 



IF (NTEMP 
IF JNCD3B 
PRINT 101 

GO TO 1090 
CONTINUE 
IF (KEEP3E 
PRINT 17 

IF (NCD3B .NE. 0) GO TO 525 
PRINT 23 

GO TO 1090 
CONTINUE 

P3E .NE. 1 .AND. SCB33 
B .EQ. 1) GO TO 535 
u x-1,MNJSS 
NPTJ (I) = -1 
CONTINUE 

NCD3E2 = NCD3B/2 
IF (NCD3B2*2 . NE. NCD3B) GO 10 9155 
- INPUT SHEAR STRESS-STRAIN CURVE ON THC CARDS 
DO 560 II = 1.NCD3B2 
PSISI 121 

HEAD 122,MIEL,NC,NPTT,ISJT,ALPH,BET,(NTAT (I) ,1=1,8) , 
2 TAUMI,GAMMT, (NGAT (I) ,1 = 1,8) 

THL .NE. MTNO) GO 10 540 



IF (KEEP3E 
IF JKEEP3B 
DO 530 1=1, 



, EQ. 0) GO TO 9154 



IF ( M: 



02669*62 

02670*62 

02671*86 

02672*62 

02673*62 

02674*67 

02675*67 

02676*67 

02677*67 

02678*86 

02679*67 

02680*62 

02681*75 

02682*62 

02683*62 

02684*62 

02685*62 

02686*65 

02687*75 

02688*75 

02689*62 

02690*62 

02691*62 

02692*62 

02693*62 

02694*62 

02695*62 

02696*62 

02697*62 

02698*62 

02699*62 

02700*62 

02701*62 

02702*62 

02703*62 

02704*62 

02705*62 

02706*62 

02707*62 

02708*75 

02709*62 

02710*65 

02711*62 

02712*79 

02713*79 

02714*75 

02715*75 

02716*75 

mum 

02719*75 

02720*75 

02721*79 

02722*90 

02723*90 

02724+80 

02725*79 

02726*79 

02727*79 

02728*62 

02729*79 

02730*86 

02731*79 

02732*79 

02733*79 

02734*79 

02735*79 

02736*80 

02737*80 

02738*80 

02739*80 

02740*80 

02741*80 

02742*80 

02743*80 

02744*80 

02745*80 

02746*79 

02747*79 

02748*79 

02749*79 

02750*79 

02751*79 

02752*79 

02753*79 

02754*79 

02755*79 

02756*79 

02757*79 

02758*79 

02759*79 

02760*79 

02761*79 

02762*79 

02763*79 

02764*79 



247 



?*-^'T 123. NC, NPTT, ISJT, TAUMT,GAMBT, 
340 CONTINUE 

54 1 PiIN ?oNTlSuI 8I " NC ' tiPTT ' ISJI ' TAUHT ' G 



PEINT 125, 

IF (ISJT 
ISJT 
ISJT 

sptt 




•Eg. 

.EQ. 
.HE. 
• LT. 



AND. 
AND. 
AND. 



.LI. 



2 .OH. 
OE. NC 



545 



1,NPTT 
HT AU (8C,I1 = 



NTAT 
NGAT 
ISJT 

NPTT 

.61. 



.BE. 
.SI. 
HNJSS' 



(NTAT(I) ,1=1, NPTT) 

AMMT, (NTAT(I) ,I=1,NPTT) 

(NGAT(I) ,1=1, NPTT) 
NE. 0) GO TO §156 
. Oj 



GO TO 9156 



NE. 0) GO TO 9 
0) GO TO 9157 
8{ GO TO 9158 

) GO TO 9159 



NGAfl (NC 
CONTINUE 

NPTJ (NC) 
JSS(NC) = 

MATSJ(N< 
ALPHJ 
BETJ ( 



NTA1(I) 
NGAT (I) 



J NC) 
(NC)' 



: NPTT 
ISJT 

= MTBL 
= ALPH 
BET 



COMMENT 

comment 

COHHENT 

comment 

COMMENT 
COMMENT 
COMMENT 
COMMENT 
COHMENT 



TAUMLT(NC) = TAUMT 
GAMMT 

() DEALS 

AND ITS SUBDIVISIONING 



_ ' ( 
GABMLTjNCl ■ GAMMT 
TGCUfi 



IS 



WITH 
FOE P 



SOBSOUTINE 

NC AND ITS . 

FOE THE PBESENT INELASTIC CASE 

CURVES WITH NUMBER CF INPUT POI 

oI!iJ H lo N ,§f EQUAL T0 BSSINL ( 

SUBROUTINE TGCUR ALSO DETEBMINE 
FROM THE SPECIAL INPUT CURVE FO 
ST3AIN HARDENING ) 

GO TO F 5^0 SJT " 2Q * 1 D * NPTT ' LE ' MSSINI - ) 50 TO 550 

550 CALL TGCUR ( NC , IABAN ) 



SHEAB STBESS-STEAIN CUEVE 
DEPOSES OF INELASTIC TEEAT 
IS RESTRICTED TO SYMHETBIC 
NTS (OF THE SYMMETRY PAST) 
= 4 AT PRESENT ) INCLUDIN 

S THE IMPORTANT INFOBMATIO 
R MILD STEEL ( HITH VIRGIN 



560 
COCMEUT 



570 

COMMENT 
1090 P 



COMMENT 



1100 

COMMENT 



CONTINUE 

- CHECK FOE UNDEFINED SHEAR 
DO 570 I = 1.NJT 

JSTT = JST(I) 
IF (JSTT .EQ- 0) GO TO 570 
IF (NJSS(JSII) .EQ. 

NC = HJSS (JSTT) 
IF (NPTJ (NC) .EQ. 
CONTINUE 

- INPUT TAB1E 3C 
il NT 9 

IF (NCD3C .EQ. 1) GO TO 8100 
IF (NCD3C . LE. .0 .AND. KEEP3C 



STRESS-STRAIN CURVE NUMBER 



0) GO TO 570 
'1) GO TO 916 



1110 



1150 
1 160 



1180 
1250 



TTOL = 2.0*TOL 

SET OFFSETS FOR STIFF TYPES 
DO 1 100 1*1. MNST 
= 1.01E20 
i = 1 . " 
SE_ 

DO 1110 
DX 
DYL 
IF (KEEP 



.LE. ) GC TO 8300 



DXS (I) = 1.01E20 
DYSJli = 1.01E20 
T OFFSETS FOB LOAD ] 
I = 1. MN 
L(I] = 1.01 
i]l) = 1.01 
P3C .NE. 1) 



. TYPES 
1=1. H KIT 
= 1.01E20 
"1E20 

PEINf-17- - ■> G ° T ° 115 ° 
GO TO 1 160 

sa = o 

CONTINUE 

P£INT F 2i SCD3C ' NE * 0) GC T ° 118 ° 
GO TO 6000 

JNTL = 
CONTINUE 

COMMENT - READ FIRST CAED IN TABLE 3C 
READ 10, NST, NIT 
PRINT 11, NST, NLT 

IF (NST . GT. MNST) GC TC 8610 
IF (NLT . Gl. MNLT) GO TC 8620 
PEINT 14 

N3CM1 = NCD3C - 1 
DO 4900 JJ = 1.N3CH1 
COMMENT - HEAD 2ND AND SUCCEEDING CARDS IN TABLE 3C 
READ 12,J1,ISTT,LTT,(J2(II),II = 1,10) 
IF (J1 -GT. NJTJ JNTL =1 ' 

NJNZ = 
DO 1270 II = 1, 10 

NJTJ JNTL = 1 



1270 

COMMENT 



IF (J2(II) .GT. NJT) JNTL = 1 
IF (J2{llj .NE. 0) NJNZ = NJNZ 
CONTINUE 

PRINT 2ND AND SUCCEEDING CAEDS IN TABLE 3C 
PRINT 13.J1, ISTT. LTT, (J2jriI),II = 1.NJNZ J 
IF J1 .LE- 0) GO TO 8200 
IF JJNTL -EQ. 1) GC TC 8500 
If IS|| .LT. .OB. LIT .IT. 0) GO TO 8710 
IF (ISTT -GT- JST .02- LTT .GT. NLT) GO TO 8720 
IF (ISTT -EQ. .AND. LTT -NE. 0) GO TO 8730 
COMMENT - NUMBER MEMBERS AND ASSIGN STIFFNESS AND LOAD TY°ES 
COMMENT - DO FOB NUMBER OF MEMBERS SPECIFIED ON ONE CARD 
DO 4500 II = 1,NJNZ 

J2II = J2(II) 
IF (J2II -LE. 0) GO TO 8200 
IF (KEEP3C .NE- 1) GO 10 4425 
DO FOB EACH 31""" 



COMMENT 



1EMBEE 



02765*79 
02766*79 
02767*79 
02768*79 
02769*79 
02770*79 
02771*79 
02772*79 
02773*79 
02774*79 
02775*79 
02776*79 
02777*79 
02778*79 
02779*79 
02780*79 
02781*79 
02782*79 
02783*79 
02784*79 
02785*79 
02786*79 
NO. 02787*79 
MENT 02788*79 
02789*79 
02790*79 
02791*79 
02792*79 
NS 02793*79 
02794*79 
02795*79 
02796*79 
02797*79 
02793*79 
02799*79 
02800*79 
02801*80 
02802*79 
02803*79 
02804*80 
02805*79 
02806+79 
02807*79 
02808*79 
02809*62 
02810*79 
02811*79 
02812 

02813 

02814 

02815 

02816 

02817 

02818 

02819 

02820 

02821*79 

02822 

02823 

02824 

02825 

02826*79 

02827 

02828 

02829 

02830 

02831*79 

02832 

02833 

02834 

02835 

02836 

02837*79 

02838*79 

02839*79 

02840 

02841 

02842 

02843 

02844 

02845 

02846 

02847*79 

02848 

02849 

02850 

02851 

02852 

02853 

02854 

02855 

02856 

02857 

02858 

02859*79 

02 860 



248 



4400 

COHKENT 
4410 



COBMENT 
4425 



4450 

4500 
4900 
6000 



C0B3ENT 



JJT(K) .AND. J2II . EQ. 
JT2JK) .AND. J2II . EQ. 



JT2(KJ | 



JT1(i 



DO 4400 K = 

IF Jl .EC. 

IF ]J1 .EQ. 

CONTINUE 

GO TO 4425 

" IST(kF M = E ISTT HZVI00SLY GIVEN STIFF AND L0AD TIPE > 

LT(K) = LIT 

GO TO 4450 
- NEB HEHBER INCEEASE Nfl 

ua = nh + i 

JT1 (NS) = J1 
JT2(EH} = J2II 
1ST (KM) = ISTT 
LT(Nfl) = LIT 



GO TO 4410 
GO TO 8250 



CONTINUE 

J1 
CONTINUE 
CONTINUE 
CONTINUE 
DO 6600 



J2II 



I = 1.NB 



'«« j. - i.nn 

ISTT = 1ST (I) 

LIT = LI (I) 



- X(J1) 

-1 131) 



6005 
6006 

6007 
6008 

6010 



COHSENT 
COMMENT 



J2I .= JT2 (I 

J1 = JT1 (I) 
COMPUTE OFFSETS 

DX = X(J2I) 

DY = Y(J2l[ 
JTSHE.NE. JSYES) GO 10 6010 
DX .IT. 0.0) GO TO 8960 
DY .LT. 0.0) GO TO 8970 

D JST2 T = JST(J2I) D * DY " 3T * °* 0) G ° T0 8980 
(JST2 .NE. 0) GC J TO 6005 

Cii J 2. —• i 

VLJ2 = 0.0 
GO TO 6006 



IF 



HLJ2 = HLJ(JST2) 
VLJ2 = VLJ(JST2 
JST1 = JST(JI) 
(JST1 .NE. 0) GO TO 6007 



HRJ1 
VUJ1 = 
GO TO 6008 
HRJ1 



0.0 
0.0 



HEO(JSTI) 
VUJ1 = VUJ(JSTI) 



CONTINUE 
IF (DX .ST. 



0.0) DX=DX-HBJ1-HLJ2 



iWfSofc 81 ' °' 0) DX-DS-I0J1-VIJ2 



6050 
6 100 



COM SENT 
COMMENT 



IF 
IF 

IF 



GO 



6200 

6300 
6600 

COMMENT 

7400 
COaflENT 



7500 
7600 



IF (ISTT ,E 
IF (DXS (1ST 
CHECK FOB T 
ORIENTATION 
EBX = 
EBY = 
(EEX . LT 
(EEY .IT 
(EfiX .S 
DXS (IS 
DYS(IS 

- TO 610C 
CONTINUE 

DXS (IS 
DYS(IS 
CONTINUE 
IF ( LTT .E 
IF (DXL(L1T 
CHECK FOE T 
ORIENTATION 
SEX 
EHY 
(EEX 
(EEY 
(EEX . - 
DXL(LI 

dylut 

- TO 6300 

CONTINUE 

DXL(LT 
DYL(LT 

CONTINUE 

CONTINUE 

DO 7400 I = 

COMPUTE LEN 
ZLSJli 



% 



HO MEB 

S 

(DX 
(DY 

. 0.0 
. 0.0 
T. TTO 
TT) = 
TT) = 



GO TO 6100 

. 1.0E20) GO TO 6050 

BEES WITH SABE STIFFNESS TYPE BUT DIFFEBENT 



S(ISTT) - 



S(I3TTJ - DY ) 

) EBX = -EEX 

) EEY = -EBY 

t .OR. ERY . GT. 
0.5* (DXS(ISTT) + 
0.5* (DYS(ISTT) + 



TTOL) 

DX) 

DY 



GO TO 8910 



TT) 
TT) 

Q. 

wo a 
s 



= DX 
= DY 



) GO TO 6300 
T. 1.0 
EM BEES 



1.0E20) GO TO 6200 
BITF 



fl SA«E LOAD TYPE BUT DIFFERENT 



IF 
IF 
IF 



GO 



.IT. 
.LT, 
, GT. 



0. 

0. 

TT 

I) = 

) = 



DXL(LTT) - DX) 
DYLfLTI - DY) 
> EEX = -ESX 
) EEY = -EEY 
CL .OS. EBY .GT. 
0.5* (DXL(LTI) + 
0.5* (DYI(LTT) ♦ 



TTOL) 

DX) 

DY) 



GO TO 8920 



DY 



DC IS (3 

DC2S (Ij 
IF (NLT.EC. ' 
DO 7500 I = 
COMPUTE LENC 
ZLL(I) 
DC II (I) 
DC2L (I) 
CONTINUE 

IDJT = 



I.NST 

■as a 

: (DX 

= EX 
= DY 
GO 
,NLT 
HS A 
(DX 
= DX 
= DY 



ND DIRECTION COSINES FOE STIFFNESS TYPES' 
SJI)*DXS(I) + DYS(I) *DYS(I) ) * + 0,5 




ND DIRECTION COSINES FOB LOAD TYPES 

llS'iSii + DYI(i,+dyi(i) ) " 0,5 



mn 

02863 

02864 

02865 

02866 

02867 

02868 

02869 

02870 

02871 

02872 

02873 

02 874 

02875 

02876 

02877 

02878 

02879 

02880 

02881 

02882 

02883 

02884 

02885 

02886 
02887 

02888 

02889*64 

02890*77 

02891*77 

02892*77 

02893*75 

02894*75 

02895*75 

02896*75 

02897*75 

02898*75 

02899*75 

02900*75 

02901*75 

02902*75 

02903*75 

02904*75 

02905*77 

02906*75 

02907*75 

02908*77 

02909*77 

02910*64 

02911 

02912 

02913 

02914 

02915 

02916 

02917 

02918 

02919 

02920 

02921 

02922 

02923 

02924 

02925 

02926 

02927 

02928 

02929 

02930 

02931 

02932 

02933 

02934 

02935 

02936 

02937 

02938 

02939 

02940 
02941 
02942 
02943 
02944 
02945 
02946 
02947 
02948 
02 94 9 
02950 
02951 
02952 
02953 
02954 
02955 
02956 



249 



CGMHENT - CQ3PUTE HALF BAND 8IDTH 07 FBAME O^Q^fi 

DO 7700 I = 1,NM 099S9 

IDJT = IABS (JTIjI) - JT2(I)) 02960 

7700 ^ffil' GT ' IDJ) ^ = ^ H | 

¥o to^oo ' 1 ' HDJT) G0 T0 8740 gflll 

8100 PEINT 31 noll% 

GO TO 9700 n?9fil 

8200 PEINT 20 09QA7 

GO TO 9700 n?9fiA 

6250 PBINT 25, ISTT,J2II,J1 02969 

GO TC 9700 02970 

8300 PEINT 30 09Q71 

GO TO 9700 0297? 

8500 PEINT 50 09971 

GO TO 9700 09974 

8610 PEINT 6 1 0997^ 

GO TO 9700 0907* 

8620 PEINT 62 09977 

GO TO 9700 0997n 

8710 PRINT 71 09979 

GO TO 9700 099A0 

8720 PEINT 72 099R1 

GO TO 9700 09QB9 

8730 PEINT 73 cr>l%\ 

GO TO 9700 099HU 

8740 PEINT 74 nitai 

GO TO 9700 099ftfi 

8910 PEINT 91,ISTI.J1,J2I 029R7 

„„ , GO TO 9700 0?9fifl 

8920 PEINT 92,LTT, J1,J2I 029S9 

GO TO 9700 02990 

8930 PEINT 93 02991*69 

GO TO 9700 09999*69 

8940 PEINT 94 0999^*69 

,„„ ■ GO TO 9700 0?99U*69 

8950 PEINT 95 0?99S*69 

GO TO 9700 09996*77 

8960 PSINI 96 02996*77 

PEINT 99,ISTI,LTT,J1,J2I 02998*77 

GO TO 9700 09999*77 

8970 PI.IKT 97 03000*77 

E2IHT 99,ISTI.LIT,J1,J2I 03001*77 

GO TO 9700 03009*77 

8580 PEINT 98 oiooq*77 

PKIHT 99,ISTT,LTT,J1,J2I 03004*77 

GO TO 9700 03005*79 

9150 PEINT 150 03006*79 

GO TO 9700 03007*79 

9151 PRINT 151 03008*79 

GO TO 97O0 03009*79 

9152 PRINT 152 03010*79 

GO TO 9700 03011*79 

9153 PEINT 153 03012*79 

GO TO 9700 03013*79 

9154 PEINT 154 03014*79 

GO TO 9700 03015*79 

9155 PEINT 155 03016*79 

GO TO 9700 03017*79 

9156 eaiNT 156 03018*79 

GO TC 9700 03019*79 

9157 PEINT 157 03020*79 

GO TO 9700 03021*79 

9158 PEINT 153 03022*79 

GO TO 9700 03023*79 

9 159 PEINT 159 03024+79 

GO TO 9700 03025*79 

31b0 PEIN'I 160, NC 03026*79 

GO TO 9700 03027*80 

9161 PEINT 161 ' 03028*80 

9700 IAEAN = 1 03029 

GO TO 9900 03030 

9800 CONTINUE 03031 

PEINT 8 03032 

COatlSNT - PRINT aESEEfi NUKB SE5, FSCH ADD TO JOINTS, LENGTHS AND OFFSETS 03033 

DO 9875 I = 1.SB 03034 



ISTT = IST(I) 03035 

IF (ISTT .EQ. 0) GO TO 9860 03036 

PEINT 7, I, JT1(I), JT2(I), 1ST (I), LT(I), ZLS (ISTT) , DXS(ISTT), 03037 

2 DYSflSTT) 03038 

GO TO 9875 03039 

9860 PEINT 6, I. JT1 (I) , JT2 (I) , 1ST (I), LI (I) 03040 

9875 CONTINUE 03041 

IF (KEEP3C ,EQ. 1 ) GO TO 9880 03042*79 

PEINT 18 03043 

GO TO 9900 03044 

y880 PEINT 19 03045 

9900 CONTINUE 03046 

kEIOHN 03047 

END 03048 



250 



************************#**#*#**** SOEBOUTINE ******************** *****#***++*+ 

SUBBOUTINE JNTDAT 03049 

COHHEKT - SUBROUTINE JNTDAT INPUTS JOIH1 LOADS AND RESTRAINTS 03050 

£S22I?,^ " i£££ LE "L cflECKS F0H BAE DATA, ACCUMULATES JOIHT LOADS AND 03051 

COMMENT - EESTBAINTS, ECHO PRINTS DATA AND PRINTS ACCUMULATED DATA 03052 

COSHENT - EQUILIBRIUM EEBCBS ABE SET EQUAL TC NET JOINT LOADS 03053 

IMPLICIT EEAL*8 (A-H,0-Z) 03054 

C03HOH /DBLK1/KEEP4L. NCD4D, KEEP4E, NCD4E 03055 

COMMON /DBLK3/ HNTVJL 03056 



3 DYY 255, DZZ 251, RXXJ25i.; BYY i 25 ; RZZ{25)' 03059 

4 EHXX 255, ERYY(25f, EEZZ{25f, QBJi2^ 

2 link: KIMjIlf sszz|25f ' Iajb - • 63062 

a C0BH 8M»l v s^flfc; SVV(25) ' DVV(25)# Efl7V<25) - 818I2:?§ 



COMMON /BLOCKS/ NPTj 20), ISJ ( 20) , NQJ '( 20 , 1 1) ,}IHJ ( 20; 1 1 , 03067 

2 NQJT(II), NWJT(11) 03068 
.COSMOS /BLKl/ TOL, ELEBNT, NJST, KEEP3C,NCD3C, 03069*79 

1 £EEP2, KEEP3A,KEEP3E,KEEP4A,KEEP4B,KEEP4C,KEEP5A, 03070*61 

3 KEEP5B,KEEP5C,KEEP5D,K22P6, KEEP7, NCD2, NCD3A, 03071*61 
| NCD3B, NCD4A, NCD4B, NCD4C, NCD5A' NCD53, HCDScJ 03072*61 

5 NCD5D, NCD6. NCD7, I?8, IP9, IP10, ITYPe' 03073*61 

6 J^AN, "OEM, NM, NJT, NST, NLT, M, 03074*61 

7 MP1, BP2, ISTI, LIT, ITYPEL,IDJ. NSTL ' 03075*61 
COMMON /BLK3/ aNJT,MNST,MSLT,HNH,HNC5,fiNC6,HDJT,HNJS,aNE,aNCS, 03076 

2 HNPCS,MNSS.KNCWH,BNJSI,BNJSS ' ' ' 03077*79 
COMHOS/BLK9/ NVLJ20.300), KT J ( 20.3 00) , NVLT(300), 03078*87 

2 NTJT(300), NPTV(20) ' BNPTF 03079*87 

COHH08 / BE / PCRflL, PCBJL, NLB^ NlBA 03080 

COMMON /ELOK1/ DCXX(25). DQYY(25), DQZZ(25), DQVV(25) 03081*69 

COfiaON /SKT2/' WEX(25'lof, SEYl25*1 0) ' CaZ?25 ' 1 0< , 03082*84 

2 HRV(25, 10), WRXl?(25,1t)f, WRYF(2$,lDf, WBTX(25.10f, 03083*84 

3 WRTY(25.10[, SETZ(25,10), WRTV(25,10 \, WKTXP (2§, 1t)f , 03084*84 

4 *RTYP(25,10J 03085*84 
COMMON /SKT3/ NCOUHT. NITEEF 03086 
COMMON /SKT19/ JCRGCN (25, 6) , JCUR£V(25,6) 03087*84 

7 FOEHAT (5X.33B SAME AS INPUT FOE THIS PROBLEM) 03088 
9 FORMAT { 49H TABLE 4A - JOINT LOADS AND LINEAR EESTBAINTS ,//) 03089 

10 FCEHAT {//,45H TABLE 4B - JOINT SUPPORT CURVE NUHBEES ,/A 03090 

11 FORMAT (//,40E TABLE 4C - JOINT S0PPO5T CUBVES ,//) 03091 

12 FORMAT (I5.5X,4E10.3,/',10X,4E10.3,20X,E10.3) "" 03092*68 

13 FORMAT ( 5X.I5.9E11.3) * ' 03093*68 

14 FCEMAT ( 25X,20H INPUT OF JOINT DATA,/) 03094 

15 FOEHAT ( 43B JOINT FCBCE(X) FORCE(Y) HOflENT(Z) , 03095*68 

i HI 1839! (VI mF s J x A SPBIN3(y) S ™ G <*> . «,„«*„ 



4H MOMENT (V) SPRING(X) 
I7H SPEINGiVJ MASS ,//) 
r 25X,23H ACCUMULATED JOI 



}§ 1215*1 i ^« 25X » 23H ACCUMULATED JOINT DATA,//) 03098 

17 FORMAT ( 48H HOLDING DATA FRCH THE PREVIOUS PEOBLEM PLUS, 03099 
. 2 15H THE FOLLOWING ,//) ' 03100 

18 FORMAT { 48H TABLE 4D - TIME VARYING JOINT LOADS - CURVE, 03101 
2 28H NUMBERS AND MD LTIPLIEES,//) ' 03102 

19 FOEHAT (4X,bOH**** LOAD REDUCTION PROBLEM - JOINT LOADS BEDUCED . 03103 

2 F5.2, 27H PEECENT BELOB LAST PROBLEH,20 ( 1 H*) ,15, 03104 

3 16H LOAD SEDUCTIONS) 03105 

20 FCSKAT { 35H JOINT NUMBERS BUST BE POSITIVE) 03106 
23 FORMAT ( 10E NONE ) ' 03107 
30 FOEHAT ( 15H HO DATA ) 03108 

32 FORMAT (15, 5X,2E1 „3 , 1 0X, 6I5,5X,I5) 03109*68 

33 FORMAT ]5X, 15 ,2E1 1. 3, 7X,€lS.5X,l$\ 03110*84 
3b FORMAT ( 30H JOINT Q-BULT W-BULT, 1 OX, 9HNSXX NSYY, 03111 

2 30H NSZZ NSW NSXP NSYP STIFF,/) 03112*68 

42 FOEHAT (5X.3I5 , 51, 1 1I5,/,25X, 1 115) 03113 

43 FORMAT {/,SX,3I5 ,/, 6fi Q,19X,11I5) 03114 

44 FORMAT 6H S 191,1115 03115 

45 FOEHAT (//,30H CURVE NUMB S YBT (1 = YES,,/, 03116 
2 30H NUHB PIS OPT = NO)) 03117 

46 FORMAT (52, 15 ,5E 1 0. 3, 415) 03118*83 

50 FOEHAT ( 43H JOINT NUMBER AEOVE GREATER THAN NUMBER, 03119 
2 20H OF JOINTS IN FRAHE ) 03120 

51 FOEHAT 1//.45H TABLE4E - TIHE VARYING JOINT LOAD CDEVES,//) 03121 

52 FOEMAT(5X,2I5.10X, 1115/(1615)) ,//; 03122 

53 FORMAT (25X,1 115/ (1615)) 03123 

54 FOEHAT (/, 5i,2I5,/,9H LOAD, 19X, 1015/ (28 X. 1 015) ) 03124 

55 FORMAT | 9H TIME, 19X^ 01 5/ (28X, ^ 015) [ 03125 
60 FOEMAT ( 40H NUHBEB OF CABDS IN TABLE 4C BUST BE, 03126 

^ 20H A MULTIPLE OF T»0 ) 03127 

6 1 FORMAT ( 40H NUKBEB OF CABDS IN TABLE 4E MUST EE, 03128 

2 20H A MULTIPLE OF TSO ) 03129 

62 FORMAT ( 48H NUMBER OF POINTS ON CUBVE BUST EE BETWEEN 2, 03130 
2 7H AND 10) 03131 

63 FORMAT (5X, 47BNUMBEE OF POINTS ON CUEVE MUST BE BETWEEN 2 AND, 15) 03132 

70 FCHHAT f 40H JOINT CUEVE NUMBER TO LARGE OR NEGATIVE) 03133 

71 FOEHAT ( 51H STIFF TYPE ABOVE NOT ONE OF MEMBER STIFF TYPES, 03134 
2 51 B STIFF TYPE 3EQUIBED TO BEFERENCE JOINT SPRINGS) 031 35 

72 FOEMAT ( 17E CUEVE NUMBER, 15, 2 5H NOT DEFINED IN TABLE 4C) 03136 

73 FORMAT 48H NUHBEE OF POINTS ON CDBVE MUSI BE BETWEEN 2, 03137 
2 7B AND 11) ' 03138 

74 FCEMAT ( 35H SYMMETRY OPTION MUST BE 1 OB 0) 03139 

75 FOEBAT ( 17E CUEVE NUMBER, I5-25H DOES NOT HAVE DISPLACEME, 03140 

2 32HNTS 155 ASCENDING ALGEBRAIC OHDEE-/, 9H WHEN, 03141 

3 30H INPUT VALUES AHE MULTIPLIED BY DTSPLACEMEST HDLTf, 03142 

4 14EPLIEE AT JOINT) ' 03143 



251 



76 FORMAT { 

77^FORMAT ( 5X, 4 8flJCINT 
* 45H(V) 

78 FCfiMAT(12X,48EMULT 
-,„^ 37H HULT 

79 FORaA?(72X,25HNUHB 

80 FORMAT (5X, 15 .5 (21, E1 0. 3) , 4 (2X?I5) ) 
FORMAT {5X, 1lHCtJRV2 NUME-'/ ' '' 



13HMUST BE C*-™* ° PTI0N = 1 ' FIEST PCIHT 0H C0EVE 

FORCE (Y) FORCE (Z) FOfiCE, 

CURVE CURVE CURVE CURVE,/) 



FORCE (X) 
TIME 

MOLT 



NUMB 



( nu 



MB NUMB,//) 



bl 



FES,//) 



2 "6Xi9HH0BB 

85 FORMAT (///) 
COMMENT - CHECK FOE LOAD REDUCTION 

IF ( NLR .EC. ) GO TO 1 100 
1A |AC = T.O - PCRJL / 100.0 
1050 I = 1,NJT 



DO 



8' 



ill: 



EEXX 
ERYY .. 
ERZZ i'Z 
ERVViI 
SXX Li 
QYY II 
QZZ 
QVV 
1050 CONTINUE 

PRINT 19 , PCRJL, NLR 
44Rrt GO TO 3100 

1100 CONTINUE 

COMMENT - INPUT TABLE 
PRINT 9 

IF I ITYPE 
DO 1110 I 
EEXX (I 
ER Y Y (I 
ERZZ |'I 
EB VV | I 
1110 CONTINUE 

1120 CONTINUE 

IF (KE3P4A 





ITYPE .EQ. 9 ) GO TO 1120 



1200 



COMMENT - ZEEd-JOINi l\%\ " G ° T ° 123 ° 
DO 1200 1=1, KNJT 
QXX(I) = 0.0 
QYY(l) = 0.0 
QZZfl) = 0.0 
avvji) =0.0 
SXX(I) = 0.0 
SYY(I) = 0.0 
SZZ(I) = 0.0 
SVV(I) =0.0 
ZHASS(I) =0.0 

PfiINT F 30 SCD4A * 0) G ° T ° 124 ° 
GO TO 3000 
COMMENT - HOLDING DATA 
1230 PRINT 17 

IF (NCD4A 
PRINT 23 

GO TO 3000 
1240 CONTINUE 
PRINT 14 
PRINT 15 

DO 2900 II = 1, NCD4A 
COMMENT - READ AND PRINT DATA FOR EACH JOINT 
SF" ' 
Pi 



NE. 0) GO TO 1240 



'■■■■«■ *••».»■ — " -i- i « a. yu in j, Vik ij0i,ii tJ W J, il A 

?AD 12, I,QXXT,QIYT,QZZT,QVVT,SXXT,SYYT-,SZZT,SVVT,ZMA 

F UI ^K^T/63lf f G8 Y Tl' c IiS6 cvv5 ' sxxi ' SYY ^ szzf ' SVTf ' z « 



CO KB EST 



IF (I „S_ 
IF (I .IE. 
ACCUMULATE 



ASST 
ASST 



2900 
3000 

3100 



3600 



3800 



3900 
4000 



QXX(I) 
iVY I = 
QZZ(I) i 

uvvm = 

SXX (if i 
SYY(l) = 
SZZ(i) = 
SlfV(I) » 
ZM&SS(I) 

COuTINUE 

CONTINUE 

IF ( ITYPE 

CONTINUE 

DO 3600 I 
EEXX (I 
ERYY [I 
ERZZ (I 
ERVV (I 

CONTINUE 

IF ( NLR .ST. 

GO TO 4000 

CONTINUE 

DO 3900 I = 
EEXX (I) 
EHYY(I) 
EEZZ (I) 
ERVV (I) 

CONTINUE 

CONTINUE 



) GO 

DATA 
= QXX 

:yy 



TO 8200 



QZZ 
CW 
SXX 
SYY 
SZZ 
SVV 
= Z 



;i; 
i 
i 
1 
1 
i 

i 

Ias: 



CXXT 
CYYT 

QZZT 
QVVT 
SXXT 
SYYT 
SZZT 
SVVT 



(I)+ZMASST 




.OB. ITYPE .EQ. 9 ) GO TO 3800 



EEXX 
ERYY 
ERZZ 
EEVV 



TO 4820 



, 03144 
03145 
03146*83 
03147*83 
03148*83 
03149*83 
03150*83 
03151*83 
03152 
03153 
03154 
03155 
03156 
03157 
03158 
03159 
03160 
03161 
03162*68 
03163 
03164 
03165 
03166*68 
03167 
03168 
03169 
03170 
03171 
03172 
03173 
03174 
03175 
03176 
03177 
03178*68 
03179 
03180 
03181 
03182 
03183 
03184 
03185 
03186 
03187*68 
03188 
03189 
03190 
03191*68 

83 1 33 

03194 

03195 

03196 

03197 

03198 

03199 

03200 

03201 

03202 

03203 

03204 

03205*68 

03206*68 

03207*68 

03208 

03209 

03210 

03211 

03212 

03213 

03214*68 

03215 

03216 

03217 

03218*68 

03219 

03220 

03221 

03222 

03223 

03224 

03225 

03226 

03227 

03228*68 

03229 

03230 

03231 

03232 

03233 

03234 

03235 

03236 

03237*68 

03238 

03239 



252 



COMMENT - tBI 
COMMENT - FOE 
IF 
IF 
PRINT 1 
PEINI 7 
GO 
U820 COH 
FEINT 1 
FEINT 1 
DO 
IF 
IF 
If 
IF 
12 
IF 
IF 
IF 
IF 
GO 
4850 FEINT 1 

2 
4860 CON 
4865 COS 
DO 



N THIS C FlcBiIa D J ° IliI DATA UNLESS IT IS T HE SAME AS INPUT 
KEEP4A ,£Q. 1) GO TO 48 20 
KCD4A ,ZQ, 0) GO TO 4865 



TO 486! 
TINUE 
6 
5 

4860 I 
QXX(I) 




1. NJT 

.NE. 




GO TO 4850 
GO TO 4850 
GO TO 4850 
GO TC 4850 
GO TC 4850 
GO TO 4850 
GO TO 4850 
GO TC 4850 



S(l) . NE.0.0JGO TO 4850 



4860 



3 'sw Q m l z\iiil X (iP ,CZZ(I) ' CVV(I) ' SXX(I) ' SYY(I > ' szz < x > ' 

TTNUE l ' 



4900 CON 
IF 
COMMENT - INF 
FEINT 1 
IF 
COMMENT - ZEE 
DO 



TINUE 

TINUE 
4900 I 
DQXX 
DQYY 
DQZZ 
DOW 
TINUE 



1,NJT 

= EBXXi 

= EEYYf 
= ESZZi 
= EEVVi 



. NLE ,NE. 
)T TABLE 4B 



) GO TO 9900 







5200 

IF 

FEINT 3 

GO TO 6 

COMMENT - HOL 

5230 PSINT 1 



(KEEP4B .EQ. 1) 
CUSVE NUMBEES 
5200 I = 1, 

I 
'I 
"I 
I 
I 



GO TC 5230 



NSXX 
NSYY 

NSZZ 
NSW 
NSXP 
NSYP 
[NCD4B 



JE, 



MNJT 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0) GO TC 5240 



000 

DING DATA 

7 



FEI 
GC 
5240 CON 

FEI 
PEI 

COHSENI - 

2 
2 



(NCD4B .NE. 0) GO TO 5240 



IF 

NT 2_ 

TO 6000 

TINUE 

NT 14 

NT 35 
DO 5900 
BEAD AND 
HEAD 32,1 
NSXP (I) , 
PSINT 33, 



N3X?(I 



5800 

5900 

6000 
COM.1ENT - 
COMMENT - 



IF 

IF 
I? 
IF 
IF 
IF 
IF 
IF 
IF 
IF 

cok: 



k 



6820 



PEI 
PEI 
GO 

PEI 

PEI 



I 

I .LE 
NSXX 
NSYY 
NSZZ 
NSW 
NSXP 
NSYP 
NSXP 
ISTJE 
_INUE 
CONTINUE 
CONTINDE 
PEINT ACC 
FOR THIS 
IF (KEEP4 
IF (NCD4B 
NT 16 
NT 7 
TO 68 65 

CONTINDE 
NT 16 
NT 35 
DO 6860 
NSXX 



II = 1, 

PEINT GN 

NSY? (li, 
I.OHJit 

NSYP{I) , 
. NJT} G 
) GO 
GT. 



NCD4B 

E DATA CARD 

«MJ(I 

ISTJR 



.GT. 
• GT, 

.GT. 
■ GT. 
. GT. 



I) + NSY 

(I) -LE. 



,WBJ( 
ISTJE 
TO 

TO 
MNJS 
MNJS 
MNJS 
MNJS 
MNJS 
MNJS 
P(I) 



NSXX(I) ,NSYY(I) , NSZZ (I) ,NSW(I) , 
(I) , NSYY (I) ,NSZZ(I) ,NSV¥ (I) , 




GC TO 8700 

GC TO 8700 

GO TO 8700 

GC TC 8700 

GO TO 8700 

GO TO 8700 

GO TO 8710 



OSOLATED 
PEOBLEM 
B .EQ. 1 
.EQ. 0) 



JOINT DATA UNLESS IT IS THE SAKE AS INPUT 

) GO TC 6820 
GO TO 6865 



o850 

2 
6860 
6865 

COMMENT 




30 TO 6850 

GO TO eeso 
GO TO 6850 
GC TO 6850 
GO TO 6850 
GO TO 6850 



PRIST _ 

NSXP (I) 
CONTINUE 
CONTINUE 
INPUT TABLE 4C 



NSYP (I) ,ISIJR ( 



^MIU/NSXXd) ,NSYY(I) ,NSZZ(I) ,NSVV(I) 



8I2H 

03242 

03243 

03244 

03245 

03246 

03247 

03248 

03249 

03250 

03251 

03252 

03253 

03254*68 

03255 

03256 

03257 

03258*68 

03259 

03260 

03261*68 

03262*68 

03263 

03264 

03265 

03266 

03267 

03268 

03269*68 

03270 

03271 

03272 

03273 

03274 

03275 

03276 

03277 

03278 

03279 

03280*68 

03281 

03282 

03283 

03284 

03285 

03286 

03287 

03288 

03289 

03290 

03291 

03292 

03293 

03294 

03295 

03296*68 

03297*68 

03298*68 

03299*68 

03300 

03301 

03302 

03303 

03304 

03305*68 

03306 

03307 

03308 

03309 

03310 

03311 

03312 

03313 

03314 

03315 

03316 

03317 

03318 

03319 

03320 

03321 

03322 

03323 

03324 

03325 

03326 

03327*68 

03328 

03329 

03330 

03331*68 

03332*68 

03333 

03334 

03335 



253 



COHMENT - 
7200 



PRINT 11 

IF J5EEF4C 



-EQ. 1) GO TO 7230 

NUMBER Of POINTS OK COBVE 



GO 10 7240 



GO TO 7240 



7240 



GO 



INITIALIZE 

DO 7200 J = 1.MKJ5 

NPTfJ) = -1 
IF (NCD4C . NE. 0) 
PRINT 30 ' 

GO TO 7 500 
COMMENT - HOLDING DATA 
7230 PEINT 17 

IF (NCD4C . NE. 0) 
PEINT 23 

GO TO 7500 
CONTINUE 
PEINT 14 
PEINT 45 

NCD4C2 = NCD4C/2 
DO 73^T^ N fe«CD4C) 

fi£aD Do%^'T^ : PNp : ^ NQJT(I, ' 

NQJfNC,I) = NQJT(I) 
N¥J Uc.lS = N8JT I 
CONTINUE ' 

NPTfNC) = NPTT 

I K1S1 S!:1iifik!!Sf: i h ,, f U«» (NC ' I} 

IF fisil Aq .V'anD, ifiSiJt .NE. 

IF f ISJT .ffl. 1 .AND. N»JT(1) .NE 

rl SSSn-A 13 *™" * 0R ' NC " GT ' MJS) GO'TO 8700 

rl l?f?l -H- I * 0E - NPIT - GT - "5 GO TO 8730 

coum - fnBl^^NE NE JNT cu!Pc) I3 ^cc H N !6s] s S8.I£iS2SS 

CALL ( IC) JNTCDR (§C?* B ° 1W0 T " COMPONENTS 



ms 



TO 
I = 



3600 
1,11) 



(N8JT(I) 



7310 



C = 1,NPTT) 

01 GO TO 8760 
. 0) GO TO 8760 

TO " 



JOINT-SUPPORT 



7350 

7500 

COMMENT 

COHiiEST 



CONTINUE 

CONTINOE 

9?2CK FOE COEVE REFERENCED IN TABLE 4B BOT NOT IN T 

DO 7700 I^"**™* VALDES N0T " ASCENDING ALGEBB 

IF (HSXX(I) Aa. 0) GO TO 7510 

NC = NSXX(I) 
IF (NPT(NC) .EC. -1) GC TO 8720 

NPTT = NPTfNC) 
DO 7505 II = 2. NPTT 

CONTINUE (I) * (<NC,II) " ""(^.H " ')). IE, 

If '"EVisttfij 0) G0 I0 752 ° 

IF (NPTfNC) .EQ. -1) GO TO 8720 

NPTT = NPTfNC) 
DO 7515 II = 2,NPTT 

CONTINUE (I) * (NHJ(NC ' II) " ""l"^ 11 " »>).«« 
IF (NSZZ(I) .EQ. 0) GO TO 7526 

NC = NSZZTI) 
IF (NPTfNC) .EQ. -1) GO TO 8720 

NPTT = NPT(NC) 
DO 7525 II = 2*NPT1 

CONTINUE (I)MNW5(NC ' IX) " NRJ ( KC ' 11 * I))-". 
IF (SSYV(I) .EQ. 0) GC TO 7530 

NC = NSVV(I) 
IF (NPT(NC) .EQ. -1) GO TO 8720 

NPTT = NPT(NCJ 
DO 7528 II = 2,NPTT 

CONTINUE lI) * (NHJ(NC ' II> " N1JJ ( HC ' 11 " I))*". 
IF (NSXP(I) .EQ. 0) GO TO 7540 

NC = NSXP(I) 
IF (NPTfNC) .EQ. -1) GO TO 8720 

NPTT = NPTfNC) 
DO 7535 II = 2.NPTT 

CONTINUE (I) * (NB(NC,II) * N «J(NC,II - 1)).LE. 
IF ( NSYP(I) .EC. 0) GO TO 7700 

NC = NSYP(I) 
IF (NPTfNC) .EQ. -1) GC TO 8720 

NPTT = NPT(NC) 
DO 7545 II = 2.NPTT 

CONTINUE^*' (NC,II) * !)8J < HC ' 11 " I))-". 

CONTINUE 

IF ( NCD4£ .LE. ) GO TO 7720 

NCOUNT ■ 1 
DO 7715 I = 1.NJT 

SUBROUTINE COEDETfl) PRINTS DETAILS OF NCK-LINEAS 
JOINT-SUPEOBT CORVES AT JOINT I. 
CALL CUEDET f I ) 
CONTINUE 
CONTINUE 

IF ( ITYPE .NE. 1 ) GO TO 8000 
COMMENT - INITIALISE TEE RESIDUAL S TEMPORAEY RESIDUAL DISPLAC 
C FCii ALL Tfifi JOItJT-SUFPOET SPRINGS 

DO 7800 I = 1,HNJT 



7505 
7510 



7515 
7520 



7525 
7526 



7528 
7530 



7535 
7540 



7545 
7700 



COMMENT 
C 

7715 
7720 



0.0) 



0.0) 



0.0) 



0.0) 



0.0) 



0.0) 



03338 
03339 
0334 
03341 
03342 
03343 
03344 
03345 
03346 
03347 
03348 
03349 
03350 
03351 
03352 
03353 
, .. 03354 
1,11) 03355 
03156 
03357 
03358 
03359 
03360 
03361 
03362 
03363 
03364 
03365 
03366 
03367 
03368 
03369 
03370 
03371 
03372 
03373 
ABLE 4C 03374 
AIC ORDEB 03375 
03376 
03377 
03378 
03379 
03380 
03381 
GO TO 875003382 
03383 

0339" 
03385 
03386 
03387 
03388 

GO TO 875003389 
03390 
03391*68 
03392 
03393 
03394 
03395 

GO TO 875003396 
03397 
03398*68 
03399*68 
03400*68 
03401*68 
03402*68 

GO TO 875003403*68 
03404*68 
03405 
03406 
03407 
03408 
03409 

GO TO 875003410 
03411 
03412 
03413 
03414 
03415 
03416 

GO TO 875003417 
03418 
03419 
03420 
03421 
03422 
03423 
03424 
03425 
03426 
03427 
03428 

EMENTS 03429 
03430 
03431 



254 



DO 7300 J = 1.10 

«BX (1,5) = 0.0 
wBTX (I, J =0.0 

war |i, j) = o.o 

SHTY (I,Jj = 0.0 

wttz h,j) = o.o 
srais (i, j =o.o 
bhv ?i,jj = o.o 

BET? (I, J) = 0.0 

WRXP ,I,J = 0.0 

BBTXEiI,a =0.0 

WHIP I, J) = 0.0 

7aoo ccrani '""f 1 ^ = °'° 

gSSSiii : ^SHiis! ViI§F3Si5S DIC1IOHS F0H iLL TflB 

EC 7 7 lo°o° 5 : ] ; r T 

7900 CONTINUE 
8000 CONTINUE 
PBINT 85 
COHBENI - INPUT TABIE 4D 
PBINT 18 

IF(KEEP4D.£Q. 1) GO 
COdUEuT - ZEHC TIflE VARYING 
DO 9950 I = 1,HNJT 



TO 9960 
LOAD CUfiVE 



NOflflEBS 



NS.O) GO TO 9970 



NFTXXl 

NFTZZi 
NFTVV* 
9950 CONTINUE 

IF{NCD4D. 
PBINT 30 
GO TO 10000 
COKHENT - HOLDING DATA 
9S60 PBINT 17 

IF(NCD4D. NE.O) GC TO 9970 
P B I N T 23 
GC TO 10000 
9970 CONTINUE 
PBINT 14 
PEINT 77 
PBINT 78 
PBINT 79 

DO 9980 II = 1.NCD4D 
LOBMENT - READ AND PRINT CNE DATA CAHD 

BEAD 4 ,I,FTHJXX(I>,FTHJYS(I) ,FTKJZZ(I) ,FTHJ VV (I) ,TTBJ (I) , 




IF( 
IF(I.LE.0)GC 



9930 
10000 



10500 



TO 8200 
.GT.HNTVJL.OB.SFTIX 
. GI.iiNTVJL. CE. NFTYY 
•GI.HHTVJL. OH.NFTZZ 
. GT.SNTVJL. CE. NFTVV 



IF (NFTXX(I 
IP (NFTYY (I 
IF (NFTZZll 
IF (NFTVV (I 

CONTINUE 
CONTINUE 

IF(KEEP4D.EQ.1)GO TO 10500 
pslN P|N c ^D.EQ.0)GC TO 10510 

PBINT 7 

GO TO 10510 

CONTINUE 
jcBINT 16 
PEINT 77 
PSINT 73 
PBINT 79 

DO 10508 



I 


. LT.OJ 


GO 


TO 


8700 


I 


-LT.O' 


GO 


TO 


8700 


I 


.LT.O' 


GO 


TO 


8700 


I 


. LT.0 


GO 


TO 


8700 



105U5 




10505 

10505 
10505 
10505 



yi?M"" fi &"»»ffl $®w - fthjvv(i) - TTaj(i) 



. 1)GO TO 11000 
KBEB CF PCINTS 
1,flNTVJL 

0) GO TO 10900 



10508 

10510 CONTINUE 
COHKESX - INPUT TABLE 4E 
PBINT 51 

IF JKEEP4E. BO. 
COfifiENT - INITIALIZE N 
DO 10800 J = 
10800 NPTV(J) 

IF iSCD4fi.MB, 
PBINT 30 
GC TO 11400 
COHKENI - HOLDING DATA 
11000 PEINT 17 

IF(HCD4E.NE.O) GO TO 10900 
PBINT 23 
GO TO 1 1400 

10900 CONTINUE 
PRINT 14 

NCD4E2 = NCD4E/2 



IN CURVE 



83831 

03434 

03435 

03436 

03437 

03438 

03439*84 

03440*84 

03441 

03442 

03443 

03444 

03445 

03446 

03447 

03448 

03449*84 

03450 

03451 

03452 

03453 

03454 

03455 

03456 

03457 

03458 

03459 

03460 

03461 

03462*84 

03463 

03464 

03465 

03466 

03467 

03468 

03469 

03470 

03471 

03472 

03473 

03474 

03475 

03476 

03477 

03478 

03479*83 

03430*83 

03481*83 

03482*83 

03483 

03484 

03485 

03486 

03487 

03488*83 

03489 

03490 

03491 

03492 

03493 

03494 

03495 

03496 

03497 

03498 

03499 

03500 

03501 

03502 

03503 

03504 

03505*84 

03506 

03507*83 

03508*83 

03509 

03510 

03511 

03512 

03513 

03514 

03515 

03516 

03517 

03518 

03519 

03520 

03521 

03522 

03523 

03524 

03525 

03526 

03527 



255 



DO 1 ^0(5 N ^' , 1 2 1^cMe2 NCD4E)SO I0 865 ° 03528 

IfAD §2, NC,NPTVV,(NVLI(I), I = 1.NPTVV) nit™ 

HSjftfi - SJ55UJ 81111 

11250 COSIIHOfi ' ' B1Ji l x > 03534 

NPTV(NC) ■ NPTVV 03535 

11200 COIIIBOB ' °3536 

PEINT 16 03537 

PEINT 8 1 03538 

lilNT 85' NC ' N?TV < NC >'<KVI(NC,I), I = 1,NPTVV) ^3540 

PEINT 55, (NTJfNC.I). I = 1 ,NPTVV1 nlliiM 

IE (NC.II.a\o£.N£.GT.aNlVJL)GC TO 8700 glfSi 

11300 CONTINUE ** T " - LT ' 2 -° E - iNETv{r - GT ' HNP " ) SO 10 8735 8j|tf 

11400 CONTINUE 03545 

SO TO 9900 03546 

8200 PEINT 20 03547 

GO TO 9700 03548 

3500 PEINT 50 03549 

GO TO 9700 03550 

8600 PEINT 60 03551 

GO TO 9700 S 3 , 5 - 5 ^ 

8650 PEINT 61 03553 

,„„„ GO TO 9700 atcIc 

8700 PEINT 70 03555 

GO TO 9700 „°5" 

8735 PEINT 63, KfiPTF Rllf 7 , 

„ , GO TO 9700 03558 

8710 PEINT 71 03559 

GO TO 9700 03560 

8720 PEINT 72, NC 81114 

GO TO 9700 slili 

8730 PEINT 73 03563 

Q „ , GO TO 9700 Still 

8740 PHIST 74 03565 

___„ GO TO 9700 Skci 

87b0 PF.INT 75, NC 21112 

GO TO 9700 03568 

8760 l&lE 76 03569 

9700 IABAN = 1 03570 

9900 CONTINUE ' 03571 

EETUBN S^^i 

"» 8 3 3 I 7a 3 

**"*s3E8o5tI5r*J«TCOrr!cT**** ROUTINE ♦**••—♦»♦♦♦..».♦*„„«„»,»♦„ 

CO KH OT - SUBHOUTIII JM&H^tj^DICOWOSEI THE NON-IINEAH Uffl 



r JOigT-SUPPOET (EASIC)'COEVE NtJHBEE NC INTOTHE COHPONFNTS 01§77 

C NOTE THAT ONLY V THE UNSCALED VIRGIN IHTEGEE INPOT COSVP Ssl-To 

SSgSiSi : *L8!g B 8Li!i S0B20D ™ «« i5 u i only CT bvbs passing Ulll 

COHhIhT " Ifl»?DT MG BSASCHES AEE ECT CONSIDERED AND HENCE SHCOLD NOT 03584 

aiw UA3 , ffi^H , |!.W l »«?»«» wares?." 1 * Hill 

/-I p^'yiHi' 1, y " «•*. ■-« » •«< *.»>. in 

e «" 4 },d» , <„ twi(20,10,. B B A M I<20,,0, 8I||§ 

NPIH1 = BPTT - 1 2|5|fi 

^ ..PTH2 = NPTT - 2 n^qs 

DO 110 I = 1,NPTT Slgil 

QQ (I) = NCJ (NC,I) Minn 

110 CONTINUE " W = " W l"^ 1 ) 8118? 

55 ioH fi -^ if§PT° H 2 ) G0 I0 205 1 

200 CONTINUE 5iUX < « = *" (I+1 > * S " Ml 

205 CCNTIHOE nilin 

,JKi"(i»88ff , S , ..7rfWf F J a ft 1 » ' < BH < NPTT > - "(BPTHi) >8Jf ? 

WWJT HC,I) = WW (1+1) Miiri 

220 CONTINUE "«*»«. ij = HBAxil) SJtl§ 

g° fl "" :Jp l «Bf S XC K f 4 !^ Ea II H I°N I iuT Ta ^ 5 V I IF «* DEE " ED »«» gjfjf 

END 03619 

03620 



256 



****^n^nn?^r^f,*:?r****rf*** SUBROUTINE **•*•••***»»*•*+,*«»•*• 



COMMENT 
C 

c 
c 
c 

COMMENT 
C 

C 

c 

c 
c 
c 



SUBROUTINE CURDET ( " JTN ' )" " ' " , """* u * i » s * 

C J8SIL44?I1-. P I«SS- T ° E DETAILS Of THE NON-LINEAR 



?f! I U Q ?,S2SS INE Is NORMALLY CALLED ONLY ONCE FOH EACH JOINT 
IN THE UNUSUAL CASE IN WHICH ADDITIONAL NON-LINEAB SOPPOBTs" 
ALE INTRODUCED (08 EXISTING ONES ASE MODIFIED) AT ONE 

lEWim X P lI N l!J G ogIs THE »«*n.3 I of T lH gSg'cSISIP*™ 



IMPLICIT SEAL * 8 (A-H.O-Z)* 

811 fill; *»**»• 

EBIY{25), 



cc 



BYY (251 
ERXX/25 
NSXX (25 
NSYP 25 



NSYYf 

ISTJ 



'HI2S/ 



l«"l« , 15TJH12 
MMON /BALA01/ QVV (25) 
RVV(25), ' NSVV{25 



RXX l25[ ' 
E8ZZ(25S, 
NSZZ(25) , 

SV7(25) , 

ISJ( 20), 



QXX(25) , 
§ZZ{25) , 
RYY (25), 
2MJ (25) , 
IHJ(25) , 

DW(25) , 



QYY(25) , 
DXX (25), 
RZZ|25) , 
BMJi25[, 
NSX£(25) , 

EBVV(25) , 



NQJ( 20,11) ,NBJ( 20,11) , 



HMAXJT (20,10) 



9 FOEHAT 
10 FORMAT 

89 FORMAT 

90 FORMAT 
1 I! 



COZ1MON /BLOCK8/ NPT{ 20 
2 NQJT(11) . NWJT(11; 

COMMON /SKi'V SBJTf20,10) , 

. COaaON /SKT3/ NCOUNT, NITER? 
2 FORMAT (10X,4(311.4,&X)) 

1QX,40fiGRIENTATIONS OF JOINT SPRING GIVEN BELOW) 
10X,49HD£TAILS OF JOINT SUPPORT CUBVES AT JOINt' N0MBEB = 

95.FOiiflAT~( 10X.27HSPEING NUMBER BEFEBS TO,/. 

2 16X,1H1.11X,8HX SPRING,/, ' /r 

J 1SX,1H2,11X,8HY SBSISG,/' 

I 16X,1H3,11x|8HZ SBB1SG,/' 

5 1oX,1H4,1U,8HV SPRING,/' 

7 16X,1g5,11X, 1t*HX PEIME SPRING,/, 

,„»'„„. , 1oX,1H6,m,14HY PBIME SPRING ( 

lO^FGRMAT ( 10x #15aS|RING G |UHB|H i |.I3,5X f 1&HHOaBEB OF COMPONENT, 

lO^FpMAT^IOX^^DEFCBMATIGNS.ix.llHEESISTANCES^X.UHSTIFFNESS OF, 

10 S FO 6Hol3lllS X /) 5fli},PaT ' 10 ^' 5HIl:P0T ' 10X ' 10HCOHPONENTS » 5X ' 7H0F C0fiP ' 
1 DO~4006 JSPE = 1,6 

GO TO ( 300 1^ 30.02., 3003, 3004, 3005, 3006 ), JSPE 

GO 10 3500 ' 

NC 



3001 



3002 
3003 
3004 
3005 



GO TO 3500 
AC 

30 TO 3500 
NC 



NSYY ( JTN ) 
NSZZ ( JTN ) 



._ = NSW (JTN) 
GO TO 3500 

GO TO 3500 ' 

NSYP ( JTN ) 



NC 



3006 

3500 CONTINUE 

IF ( NC . EQ. ) GO TO 40 00 

NPTT = NPT (NC) 

NPTM1 = NPTT - 1 
DO 3600 I = 1,NPTT 

C2 (I) = CRJ (JTN) * NCJ (NC,I) 
r „ , i w ij) = HHJ (JTn[ * NWJ hCl) 
IF ( I . EQ. NPTT ) GO TC 3600 

RMAX (I) = CkJ (JTN) * EMAXJT (NC,I) 



3600 CONTINUE 

PRINT 10 
IF ( 

PRINT 8 9 

PRINT 9 

PRINT 95 

PBINT 10 
3700 CONTINUE 

PRINT 90, JTN 

PRINT 9 

PRINT 100, JSPR, NPTH1 

PRINT 9 

PRINT 104 

PRINT 106 

PEI2JT 2 

DO 3800 : iPTT 



NCOUNT .NE. 1 ) GO TO 3700 



1 UD 

-« »« (1), GQ(1) 
5800 I = 2,NPT'. 



3800 PRINT 2, WW (I 



STF = 3KAX~ (1-1) / WW (I) 

IT?. RMAX(I-l) 



tOOO CONTINUE 
RETURN 
END 



NCOUNT 



iQil)', S5 

= NCOUNT +" 



********** 
03621 
03622 
03623*84 
03624 
03625 
03626 
03627 
03628 

03629 
03630 

03631 

03632 

03633 

03634 

03635 

03636 

03637 

03638 

03639 

03640 

03641 

03642*70 

03643*75 

03644 

03645 

03646 

03647 

03648 

03649 

03650 

03651 
,03652 

03653 

03654 

03655 

03656 

03657 

03658+84 

03659*84 

03660*84 

03661 

03662 

03663 

03664 

03665 

03666 

03667*84 

03658*84 

03669 

03670 

03671 

03672 

03673 

03674 

03675*84 

03676*84 

03677*84 

03678 

03679*84 

03680 

03681 

03682 

03683 

03684 

03685 

03686 

03687 

03688 

03689 

03690 

03691 

03692 

03693 

03694 

03695 
03696 
03697 
03698 
03699 
03700 
03701 
03702 
03703 
03704 
03705 
03706 
03707 
03708 
03709 
03710 



257 



SOBBOUTINE ************************* 



******************** ************** 
SUBROUTINE RDKST 
SSSUsJiS " SUBROUTINE 3D3ST INPUT5 MEMBER STIFFNESS DATA fTABLF 51 

gS8S5iii : ^o E f K D s i N I?!s B A A g D c t^& c ^II!I s D i?I DT ^™cII T T 4 c . ( 5ISSL 5 > - 

I HP LICIT iiEAL*8 (A-E,0-Z) 
25) 



DIMENSION NOT]: (23)' 
COSMOS /BLOCK2/ DXS ( 

2 DC2S ( 2 5) , 

3 PRAGJ25), 

4 IO?OP{ 25), 
NAL( 25) 



. 25 
PRFf 25 
ELEHN(25) , 
IPINL{ 25), 



Hi 



DYS( 25), 
IE( 2$/, 



PRAj 



ZLS( 25) , 
QM( 25) i 



5 BSXE ( 25) , 

COMBOS /BLGCK4/ 



2 JT1 (SO) , ou 

. COBMON /3L0CK5/ XLS, 
2 SXLf 50). ' SIL 

CCHaCN /BALA 12/ SHC/2 
COMMON /BLOC 12/ SB (20 
11(20,10) 




I PI BE ( 
NSYL " 
HSZH 
SKC(5 



H ( 25 

m 

TM(50 



NITMfSM 
XfiS ( 50' 
SZL 



1 181 



NC51 
NSZL 
NCDS , 
IST(50) 

' rl" 



25 
25 

25 



3» » 



DCISf 25), 
BB( 25)," 

INLOP ( 25) , 
NABf 25) . 
IAXC?S( 25) 



IT (501 , 



iac(50) 

AELf 50) , 



*„ YI(20,10) , NSS<2D,10) 

common /balai3/ gsjob) 

common /3loc13/ npts( 08), 

2 NSIT(11) . ' NEPT(11) 



onizu, iuj , E«(20,10) , 
BSSj(2p,10) , NA(20f, 

ISS( 8) , 



BI{20,10), DI(20.10), 
BC6a(20), IBECT(i0,l6) 



HSIG(0 8, 11) ,BEPS(0 8,11) , 
NQH (20,11) , N«H(20,11), 



6 
7 

8 

9 

12 

13 

14 



EPSTHD(8) , 



BSIT7TT) ,' Sept 111" ' 

COMMON /BLGC14/ NPTMl 20), ISB( 20) 
2 UQMT(11), NHHT 11) l ' 

COMMON /BLKl/ TOL, SL£BNT,NJST,, KEEP3C, NCD3C, 

2 K£EP ^£ ^2EP3A,KEEP3E,KEEP4A,KEE?4a'KEEP4C.KEEP5A 

3 KEEP5&,KEEPSC;kEEP5D;kSEP6, KEEP7,BCD2; 'NCD3A ' 
3 NCD33, NCD4A, NCD4B, NCD4C' NCD5a' NCD5B. NCD5C 

5 '??g5 D » »CD6, NCD7, IP8, ' IP9, ' IP10,' ITYPe' 

COMMON /SKT 10/ KDIV(20,10), NPCTOT(2Q) 

common /sktii/ assik, ' " mssibi ' 

COMMON /3KT30/ MSTIF(25) , BIOAD(25) , MODEL(25) 
^COHHOK /3KT31/- ALPHA 1 f 8 ,' BETA U) ', SBLSLP(8 
SLOPHD j|j SIGOLTJeJ; MATBL M 
','Wi V&\ 12 " SUPPORT CURVES' FOB KEMB2ES,/) 

/,36h TABLE 5C - SIEESS STEAIB COEVES./) 

/ f,ni U n-,I ABL f 5B " CBOSS SECTION DATA ,A 

S9I ma TABLE 5A - MEMBER STIFFNESS DATA , /) 
2I5,E10.3,A5,5X,2B10.3,6IS) ' '' 

/I5, E10.3,2X,A5,2X,2E10.3,4l5, 5X.2I5) 
//, 48H STIF #OF MGD OF ELEMENT PRISMATIC PEISBATIC 
35H BON HOHB AXIS ODTPOT PIN PIN , /, ' 

48H TYPE ELEH ELAST TYPE I ' A 

ioxf}iio'5f CBDS 0J?T 0PT FH0H T0 '//> 

5 llfl THE loLLOHING ATA /f E ° a THE PEETI0DS "OB.LB8 PLUS, 

i^'^ raoS T " F ' T % I5 ' 6H cc f D ' 5X ' / ' a 

30H SX SY SZ,/) 



FCEfiAT 
FOEHAT 
FOEKAT 
FOE3AT 

FoaaAT 

FOEBAT 
FOEHAT 



.{ 



15 FOSMAT 

16 FOEHAT 

17 FOaaAT 



18 FORMAT 
2 
3 

13 FOEHAT 
20 FGEiiAI 

2 45fl 

3 50H 

4 26H 
23 FOEHAT 

FORrfAT 
FG&8AT 
FOEBAT 
FOB a AT 
FOEHAT 
FOEHAT 



(10X.4I5,5X,4I5,5X,2E10.3) 

STIFF TYPE, 15, 6H CONT ,/ 



30 
31 
32 
33 
34 
35 



10H 
25H 
51H 
35H 

45E 
40B 
48H 



TO JOINT ,/, 
NSZ KA NSX NSY NSZ, 

BDLT,/, 5X,4I5,5X,4I5,5X,2E11.3) 



FROM JOINT 
NA KSX NSY 
OLI ri - 

NONE ) 

NO DATA IN TABLE ) 

NIJHBEE OF CAEDS TO FOLLOW MOST NOT BE NEGATIVE) 
OUTPOT OPTION MOST BE OH 1 I nt^AAiVE) 

III ??SIS! SSII^IOT BE GREATER' THAN ONE ) 



NON LINEAR OPTION MOST BE 9 OS 1 
CROSS-SECTION NOHBEE TOO LAEGE OR 



41 FORMAT 

42 FORMAT 

43 FORMAT 
2 

3 SX, 

4 2X 

44 FOEKAT ' 
FORMAT 
FOHMAT 
FOEHAT 
FORMAT 
FORMAT 
FORMAT 
FOEHAT 



25HSECTICS |plEB~|?|ciflBD )" 

riCN 



[ii'.lxs) INPtJI 0F c 

(5X^50HCBOS NOME SUB K 



NO CECSS-, 



BOSS SECT] 



// ) 



45 
46 
47 
51 
52 
d3 

54 



36H SIG-EP 
4SBSECT CED3 
4HK0aB,/) 
"(li'2X) 



IDTH OR DEPTH OH I-CENT RECT =0- 

SIG-MOL EP-MUL SH-CCEF,/, 



DIV O-DIA THICKNESS 



PIPE=1, 



55 FOEHAT 
2 

56 FORMAT 
2 

3 

57 FORMAT 
2 

3 

58 FOSMAl 
60 FOEHAT 
6 5 FOHMAT 
67 FOEHAT 



5X, 2(I3\2X) ) 

5X.I5, 3E1013' 215, 3E10.3 ) 

ill* th U' illhi' m- §i» 3eio.3 

15X, A1, 2X, 3E10.3, 215, 51. 3E10.3 
35H STIFF DA1A BUST START AT 0.0 

IRi fllfl DATA MOST STOP AT END OF HEMB) 

50H STIFF SEQUENCE MUST BE LOSGEE THAN 1/B *SPAN 1 

STIFF EAfA MUST BE SPECIFIED CONTINUbuSLY,IE ' 



). 



( 



35 H FHOB DIST MUST EQUAL LAST TO DIST 

To! specIf^dT 3 IN TABLE 5 B ° T STIFF T 

III STIF A ^YiIs BDS N0| P I^E?i!l D ED F ?^ TABLE 5 



IPES NOT ALL, 
BEAD BUT ALL, 



47E 
48H 
5H 
47H 
35H 
50H 
45H 
50H 



CHECK CARD COUNT AND" NUMBER OF S^IFF TYPES! 
D - S n AL / L STIFF TYP£S SPECIFIED BUT ALL CAEDS NOT, 

CHECK CARD COUNT AND NUBBEE OF STIFF TYP^S) 
AXIS OPTION MUST EQUAL 1 OR 2 I nf-i) 

ARE NOT PEEMITTED) 



NEGATIVE VALUES OF A 



II 2ND CARD USED FOB STIFF TYPE, PBISHATIC I 



******** 

03711 

03712 

03713 

03714 

03715 

03716 

03717*42 

03718*42 

03719*42 

03720*42 

03721*42 

03722*42 

03723 

03724 

03725 

03726 

03727*51 

03728 

03729 

03730*50 

03731 

03732 

03733 

03734 

03735*79 

03736*61 

03737*61 

03738*61 

03739*61 

03740*61 

03741*61 

03742 

03743*79 

03744 

03745 

03746 

03747 

03748 

03 74 9 

03750 

03751 

03752 

03753**8 

03754**8 

03755**8 

03756**8 

03757**8 

03758**8 

03759 

03760 

03761 

03762 

03763 

03764 

03765 

03766 

03767 

03768 

03769 

03770 

03771 

03772 

03773 

03774 

03775 

03776 

03777 

03778 

03779 

03780 

03781 

03782*48 

03783 

03784 

03785 

03786*48 
03787*48 

03788*48 

03789 

03790 

03791 

03792 

03793 

03794 

03795 

03796 

03797 

03798 

03799 

03800 

03801 

03802 

03803 

03804 

03805 



258 



til FCSdAT 
2 

71 FOSMAT 

72 FOEfiAT 
2 

73 FOEfiAT 

74 FOfiHAT 
2 

75 FORMAT 
2 

76 FOfiHAT 

77 FCBHAT 
2 

78 FCBHAT 
2 

79 FCBHAT 
2 

80 FCBHAT 
8 1 F02MAT 

2 
82 FOBMAT 
S3 FOEJiAT 

84 FOfiHAT 

85 FOBMAT 

86 FOBHAT 

87 FOfiHAT 

88 FOBMAT 
2 

89 FOSBAT 

90 FOBHAT 

92 FOBHAT 
2 

3 

93 FOSMAT 

95 FOBHAT 
2 

3 

5 

96 FC82AT 
2 

3 
99 1 F02HAT 

993 FOSHAT 
2 

3 

994 FCBHAT 

2 15, 

3 

4 

996 FOBHAT 

997 FOBMAT 
2 
3 

101 FOSHAT 
2 
3 

103 FOSMAT 
2 49H HA 

104 FOBHAT 

2 56H an 

3 10H IN 

105 FOBMAT 

2 57H HO 

3 26H TO 
107 FOSHAT 

2 
109 FOBHAT 

2 16HEXC 
120 FOSHAT 
130 FOBHAT 

2 51 H HO 
140 FOBHAT 

2 5X.35E 
200 FOEMAT 
20 1 FOBMAT 
220 FCBHAT 

2 
230 FOBHAT 

240 FOBHAT 
2 

241 FCBHAT 



OF STIFF, 

- iVEN) 
IF NOHBEB OF, 



20fi AND A HOST BE 0.0 I 

( lOhSCME DATA )" 118248 °^ l0fi = '' TABLE SE fltIST HATE 

( ini ZZ 1FF TTPES MOST NOT BE NEGATIVE 

1 18g TYP E I T IIIc?li P ! D GREfl f £a THAN WHraan 

I P| f „ j^^fNE^B^I^of'HA^lol^l 80 " ' 
2=H CABDS THAT FCLLGHS IS ) 

> ^nS ^5S A r 0PII0K HDST BE 1 OE 0) 

{Slnu o§ no L ^uIve KI! s F P C Ici S Ii 2 |f-f TBAIN CUE7E N0 ' 

||I OB NO HD £l B f R ES CF sI£c E l1iED OF f S ° SS » CTI0H T ° " BGE ' 
*fl AND fi 8) 8BEH ° F P0IJi,IS 0K COBVE MOST BE 3ETHEEH 2, 

( 40H SYMHETfiY OPTICS MOST BE 1 OB 

(/,5X,28HHATE COEVE NOHB SYMT (1=YES 

'AUY.m 2 N E D ?0 B .3fIl5°L T *0 ."f?i 



) 



/,5X,26HNUBB 
5X, 315, 5X, 



PTS CPT, 
1115. /, 25X, 



= NO f) 

, Ji.o, ax, nib, /, 25X, 1115 ) 

J A?|A J;H fiBEE ' J5, 10H NOT INPUT) 

16a AEEA N0MBEE,I5. 16H AND ARF» HflWBJJB TS 

40H SHOOLD HAVE THESAME NOMBER OF PIECES '/ li 



45H siHcri3|r4|rBo?roi u Jiii|if §f li! FP '^!l:i 5 , 

10H NOT INP0T) 



31H 
32B 



STBESS-STBAIN COBVE N0HBEE,I5, 
STRESS-SIBAIN COEVE NUMBEBstlS, 



( 



( 



Jfc aiKJSSS-SXB&IB COEVE NUMBFBS TS UH inn tK 

3SH SHOOLD HAVE THE SAME N0MBEE CF POINTS 5 5X ' ' 

36H SINCE THiiY AEE BOTH ON PIECE NOMEEfilS ' ' 

16H OF ABEA NUMBERS, 15, 4H AND IS 5 It * 

35H WHICH ABE CN HEMBEBS OF STIFF Type' 1 5 \ 

13 J f^ C ^ NUBBE ?f 15 ' 15H ON ABEA NOHbIb,i5, 

4H AND, 15, 24H HHICH ABE ON STIFF TYPE 15/ 5Y 

40H CANNOT BE BOTH A PIPE AND A BECTANGLE ' \ ''' ' 

3oS 2ISI ER S _B CDRVE N0MBEfi,I57l0H NOT INPUT) 

298 MEMBEB Q-ft COBVE NOBBERS .15 4H AND ^g^ ui > 

38 B SHOOLD HAVE THE SAME NOBBEB CF POINTS / 5X 



PBINT 9 
IF 

FEA 
IF 

IF 
IF 



oTn SiS^ £ AnJSI A-n-C u« nEBBEBS OF STIFFNESS TYPF T5l 
27B STBESS-STBAIN COBVE BOBBEB.I5. 16H ACTING ON PIEC* 
10B OF ABEA ,15, 11H STIFF TYPE. 15./. 

tlS aSIebIIic ^IIe P ) I8AL VALDES 6f ^ eaih ih »sc«di«. 

( 2?h BiFsssavrsg = 1 - fiest pciht on cuavE - 

( || »»3JS: 3§I POfiI ^| V In?oFIIt H 5 FIn1! SJLgH'Sf. 

,rv 5ll DISPLACEMENTS IN ASCENDING AXGEBEAIC OBDEB) 
(5X,35E TOTAL NOHBEB OF LAYEBS IH X-SECT #,IS,/,5X, 
17H EXCEEDS LIBIT OF,I5./,5X, »/»=>*# 

je 30HNOIE : EACH PIPE HAS 10 LAYEBS ) 

X, 10BSTIF| TYPE,I4,17H AND PIECE NOBBEE .14 ,/,5X, 
VS DIFFERENT # CF LAYEBS AT FBOK AND TO j6lNTS ) 
(5X.10HSTIFF TYPE.I4.12HPIECE NO HBEB ,14 ,/, 5X, 
ELASTIC) SIG-£P COEVE # AT FEOH AND t6 jSlNTS SINCE, 

(5X.10HSTIFF TYPE,I4,12HPIECE NOHBEE . 14,/, 5X , 
4 So!MI Il^ E S BI!fsfe) SIEAIN HDLTIP " EBS *^ ^°« ^D, 
(5X, 12HCBOSS-SECT #,I4,8H PIECE J, 14, 9H SIG-EP #.I4./.5X. 
<= 34H HOST BE SYfiKETBIC SINCE INELASTIC ) ' ''' ' 

(5X, 128CS0SS-SBCT #,I4,8H PIECE t,I4, 9H SIG-EP #.14./ 5X 
£EDS LIMIT OF,I4,13H INPUT POINTS ) ' ,/,:l ' 

(5X,34HN0KBEB OF ELEMENTS MOST BE > 4 £ < ,15) 
(5X,26BALL BISBEES SITH LOAD TYPE. 15,/, 5X, 
ST HAVE SAME # OF ELEMENTS FOE IEEIE STIFF TYPES) 
(5X ^f,? li 5 fiV A L IE SIG-EP INPUT FOB X-SSCT CF STIFF TYPE. 13./. 
ALPHA = AND BETA # NOT PERMITTED ) '"'"''' 

f^ifl°3) 8 ° D C? PRISMATIC,/, 19B RIGIDITY SHE.AEEA,//) 

SHEAl E AEEA 7 f TA1UES A3E NCT PERMITTED FOE A, I AND, 

IF INLOET=1 PBISHATIC I AND A MOST BE 0.0 
„ TrrT SHS BEH 9 F CABDS IN THIS TABLE SHOOLD BE, 
DIVIDED BY 3 TO OSE SHEAB MODEL ) ' 

(//.7H HOD CF,/.9H EIGIDITY,//) 
DATA IBLNK /2H -/, MTNO /4h / 

DATA SHEAR /5HSHEAB/ 



50H 
12H 



hi 



,_iH 
33H 



) 



IF (KEEP5A .22-0) NSTL 
COMMENT - FEAHE HOST HAVE AT LEA 



PRINT 1 
PBINT 2 
GO TO 6 



SCD5A .La 
NCD5A . NE 

(SST . 1,E. 
NCE5 = 

7 

3 

100 



AND. 



0) GO TO 1 150 
NSTL) GO TO 8550 



= 
SI ONE STIFFNESS TYPE 
KEEP5A . LE. 0) GO TO 8300 



03806 

03807 

03808 

03809 

03810 

03811 

03812 

03813 

03814 

03815 

03816 

03817 

03818 

03319 

03820 

03821 

03822 

03823 

03824 

03825 

03826 

03827 

03828 

03829 

03830 

03831 

03832 

03833 

03834 

03835 

0383 6 

03837 

03838 

03839 

03 84 

03841 

03842 

03843 

03844 

03845 

03846 

03847 

03848 

03849 

03850 

03851 

03852 

03853 

83ISS 

03856 

03857 

03858 

03859 

03860 

03861 

03862 

03863 

03864 

03865 

03866 

03867 

03868 

03869 

03870 

03871 

03872 

03873 

03874 

03875 

03876 

03877 

03878 

03879 

03880 

03881 

03882*84 
03883*84 

03884*35 

03885*35 

03886*47 

03887*47 

03888*47 

03869*84 

03890 

03891*16 

03892 

03893 

03894 

03895 

03896 

03897 

03898 

03899 

03900 

03901 



259 



1150 CONTINUE r,-, on -, 

NC51 (1) = -1 03905 

g|]Jf[. - I 1 03906 

12,0 PHINX^ 1 "° §||8| 

1250 CONTINUE "910 

PIUNT 14 0391 1 

NCR5 = 03912 

COMMENT - DO FOE EACH STIFF TYPE nllU 

DO 5900 JJ = 1 NST 03914 

COMMENT - SKIP FOfi STIFF TYPE PBEVIC3SLY DEFINED Sllll 

I ^fi^lfioTO 1 ^^ 105900 §}{} 

S8MIK : iiilf g;iiiili; c -y r ¥i JP** ™ » — « «» 11 u 

1300 CO F N^ C S g! (JJ " 1 > - GT - °> P ™ » , Ojfli 

COMMENT - eU^d" pi&T^l^fg I8 B 8 Iti°F F TYPE \W% 

2 EAD IPINLT S IpfNBT T ' E ' ELEaNT ' PBIT ' PHAT ' IliL0PT ' NCDST ' IAX0PT ' I0P0PT ' 03926**8 

IF ( MSTT . EQ. ) MSTT = HNE r)W)l** Q 

2 IPINLT^illNBT ' £ ' ELEKNT ' PEIT ' PEAT ' : ™LOPT, NCDST, IAXCPT,IOPOPT, 03929**8 

g | til :3:.2.| G G ° ic c 1118 Sllil** 8 

i 1 ! teBr.riJ-oJ g6°!o 5H8 m - gt - 2 > G0 M 8580 §||li 

Willi :g l t t : ?, ag H 4e I 8SS5 T - GT - 1) G0 T0 8320 ] 

IF [IPINE1 .GT. 1) GO TC 8330 n\%\% 

IF ^iv^vf • inlopt - gt - 1) go to 83< *° o||II 

?I f^™ fiE ™ ISTT l GC TC 86S0 03940 

IF flSIT .SI. NST) GO TC 8720 n\lV\ 

,„»., , IF JISTT .LT. 0) QO TC 8710 n^oao 

COflKEKT - MULTIPLY A AND 1 BY E 9\ll\ 

JPSFT = E*PEIT n\lll 

r ^ PEAEI = E*PBAI n\Vt% 

IF ISTT .20. ) H = SHE S||SI 

IF ISTT ,EQ. GO TC 1350 Clllal 

MSTIF^STT) = HSTT §3947 

1350 CONTINUE °"^n 

HP2 = a + 2 3951 

( ELEHNT .EQ. SHEAR ) GO TO 5200 nTql^*»s 

NCDST .GT. 0) GO TO 2400 MIU 8 

„ , ii jINLOPl .EQ. 1} GO TO 8740 nioiS 

COrtSEHI - PElidATIC aSKBEE - NC CARDS FOLLOH glff| 

CO«»t - MoiI S T F I KE ^AE?^EAD !N ?*tlh' U ' ^ G ° TC 366 ° || 

PHFVlSTT) = PEFT niqiq 

PRAE(ISTT) = PEAET (nqfin 

ncds]istt[ = 81119 

IAXCisjISTT) = IAXOPT ^|?4 

IOPOP(lSTT) = IOPOPT aitti 

IPISL ISTT) = IPIKLT Pjflfrf 

IPINEflSTTj = IPINRT „,%? 

INLOE(ISTT) = INLOET Clitf.fi, 

GO TO 5900 atIct 

2400 CONTINUE 2"67 

1F CP S?5 s -(!IiT?-2 N cg s E T PBAE1 - GT - °- 0) G0 T0 867 ° gifll 

lAXOPS(ISTT) = IAXCPT §||4? 

lOPOP(ISTT) = IOPCPT 0397? 

IPINLilSTT = IPINIT Qiq7T 

IPINEflSTTj = IPINRT 0397U 

rm t INLOE(ISTT) = INLOPT Ctiq4t 

IF (INLOPT .EQ. 1) GC TC 5100 niQTt 

SS555'" ~ £SJLI H Jf BATlc aEIIBEE - NCDST CARDS FOLLOW 03977 

COMMENT - STORE TEHPOBARY READ IN VALUES 0T97R 

PRINT 18 ISTT ujy/o 

COMMENT - DO jfiB EACH ADDITIONAL DATA CARD FOE THIS STIFF TYPE 03980 

NC5 = NC5 + 1 Mini 

H fi^ EQ - 1 ) SC51(ISTT) = NC5 03983 

IE (NCH5 .EQ, NCD5A) GO TO 8560 n^qsu 

C03aENT - EEAD AND PE INT NON PRISMATIC STIFFNESS VALUES nioo? 

2 3EAD s^' ( Ncsf (NC5) ' XRS (HC5) '*M»cs"Si(Sci) IsxlTncS) ,syl ( nc5) , ^le 8 6 

2 ?RIN S2MNC5) (NC5,,XHS(NC5) ' FL(1IC5) ' AE:L(NC5) ' SXX ( NC5 )' SYL ( SC5 )' 03988 

NCH5 = NCB C + 1 03989 

^I A p E iY^ 5) AND L !-B?i ' CE - FL(HC5) " LE - °-°^ GC T0 8660 iii!3 



COMMENT - Mt 



03992 



FL(NC5) = E*FL(NC5) nilqi 

COMMENT - CBC^fSila UAT E A* AEMfib) »|||| 

rB Til = ZLS<ISTT)/K O^qqfi 

If (II .EQ. 1) GO 10 3200 03997 



260 



3200 
3300 

4000 

4500 

COHEEKT 



II 
IF 
GO 
If 
IF 
IF 
CON 



TO 4000 5 " 1) * TH * GE * * ES < NC5 > 
(XLS(NC5) „ HE. 0.0) 

XRSh>c5) -EQ. 0.0) 
JXLS JNC5) + 1H .GE. 

INU 



TO 8540 

) GO TO 8530 



um 



GO TO 8510 
GO TC 4000 
XBS(NC5) ) GO TO 8530 



5100 

COMMENT 

BEAD 
2 



CONTINUE 

CHECK FOE STIFF NOT STOPING 

ESBLN = iZLS(ISTT) 

IF (EBELN . LT. 0.0) EEBLS = 
IF (EBHLN , GT. 0. 1*TH) GO TO 

XES1NC5) = ZLS(ISTT) 
GO TO 5900 
CONTINUE 
INPUT NONLINEAR SUPPOBT CUBVE 



AT END OF HEHBE8 
- XHS (NC5) ) 
-EEBLN 
8520 



AND CBOSS-SECTION NUMBERS 



„_JI* B*i (ISTT) ,NSXL(ISIT),NSYL (ISTT) .HSZL(ISTT) ,NAE (ISTT) , 
NSXS (|STT),NSI|{ISTT) ,NSZR(ISTT)\QB(ISTT),s5fl<ISTT) l ' ' 



j200 




GT. HNCS .OB. 

.LT. .CS. NSXL(I"STT 

•LT. .OB. 

CE. 

OE. 

CB. 

CE. 



.LT. 
• LT. 
.LT. 
.LT. 



iNAL(ISTTf 

i NSXL (ISTT 

NSYL(ISTT 

iSZL i ISTT 

JSXB I ISTT 

iHSYBi ISTT 

i NSZfi i IS1T 

TO 5900 

CONTINUE 

IF (INLOPT .EQ.1 ) GO TC 5240 
PEINT 200 
BEAD 201, G.PRSHA 

NCB5 = NCE5 + 1 
PEINT201, G,PBSHA 

PEAG1 = G*PRSHA 
IF { (PEFT .LE. 0.0 .OB. 
* GO TO 9220 

COMMENT - STORE TEMPORARY EEAE IN VALUES 
PfiF(ISlT)' = PEfT 
paAE(ISTT) = PEAET 
PSAG(ISTI) = PEAGT 
NCOS (ISTT) = 1 
IAXOPS(ISTl) = IAXCPT 
IOPOP(ISTT) = IOPCPT 
IPINI(ISTT) = IPINIT 

IPINE(ISTT) = IPINBT 
INLOP(ISTT) = INLOPT 
ELEMN(ISTT) = ELEHNT 

GO TO 5900 
5240 CONTINUE 

IF (PBFT .GT. 0.0 .OR. P2AE1 
NCDSjTSTT) = NCDST 
IAXOPS(ISTT) = IAXCPT 
lOPOP(ISTT) = IOPOPT 
IPINL(ISTT) = IPINIT 
IPINE(ISTT) = IPINET 
IuLOP(ISTT) = INLOPT 
ELEHN(ISTT) = ELEBNT 



ISTT) ,NSZL (ISTT) , 
(ISTTf ,QH (ISTT) ,HB (ISTT) 
.LE. 6} GO TO 6350 ' 

NAB(ISTT) .GT. HNCS) GO TO 8350 

HNQHS 
HNQWH 
HNQHB 
MNQHH 
HNQHB 
BNQHH 



NSYLflSTT 
NSZL (ISTT 
NSXB(ISTT 
NSYBflSTT 

bszhJisti; 



, GT. 

GT. 
, GT. 

GT. 

GT. 

GT. 



GO TO 8750 
GO TO 8750 
GC TO 8750 
GC TO 8750 
GO TC " 
GC TO 



8750 
8750 



PRAET .LE. 0.0) .OB. PEAGT .LE. 0.0) 



,GT. 0.0) GO TO 9230 



COaaBSI - INPUT NONLINEAR' SUPPORT CUBVE AND CROSS-SECTION NUMBERS 

READ 19, NAL (ISTT) , NSXL (ISTT) , NSYL (ISTT) .NSZL (ISTT) ,NAR (ISTT) , 
2 KSXR (ISTT), NSYK (ISTT) ,NSZB (ISTT), QB (ISTT) ,«M (ISTT) 

NCE5 = NCE5 +1 
PEINT 20, ISTT, NAL (ISTT) , NSXL (ISTT) 



5900 

COflflENT 
COHSEilT 
COBHENT 

5950 



NA3 

IF 

IF 

IF 
IF 
IF 
IF 
IF 
IF 
CON 



§TT) 
BflSI 



_ TT),NSYL (ISTT), NSZL (ISTT), 
ISTT) ,NSXE (ISTT) ,8SlS (ISTTf ,N SZfl (ISTT) ,QH(ISTT) ,B 
NAL (ISTT) .LE. 6 .OB. NAR (ISTT) . LE. 0) GO TO 835 
NAL (ISTT$ .GT. HNCS .OR. ' 
NSXL (ISTT) .LT. .CB. NSXL 

•LT. .CE. NSYL 

•LT. .CE. NSZL 

-LT. .CE. SSXB 

.LT, .CE. NSYS 

•LT. .CB. NSZH 



NSYL 

NSZL 

NSXis 

NSYR 

NSZE 

INUE 

IF (NCE5 .LT. 

THE FOLLOWIN" 



ISTT) 
ISTT) 
ISTT) 
ISTT) 
ISTT) 



NAR(ISTT) 
(ISTT 

I 'ISTT 
i'ISTT 
list t 
ISTT, 
(ISTT) 



GT. 
. GT. 
. GT. 
. GT. 
. GT. 
. GT. 
. GT. 



BNCS) 
MNQSB) 
KNQHH) 
KNQHH) 
BNQWS) 
HNQHB) 
HNQHB) 



K (ISTT) 

50 
GC TO 8350 
GC TO 
GC TO 
GO TO 
GC TO 

TO 

TO 



GC 
GC 



8750 
8750 
8750 
8750 
8750 
8750 



NCD5A) GC TC 8570 

STATEBENTS (OPIO STATEMENT 6000) SET THE VALUES 



- FOS NUH OF ELESENTS BY LOAD TYPE EQUAL TO THAT INPUT BY STIFF 



5990 



6000 

6100 

COHHENT 



TYPE: AND ALSO CHECKS 
DO 5950 K = 1,NLT 

NOTE(K) ■ 
6000 JJ = 1.NM 

ISTT = 1ST 

LTT = LT 

LTT .EQ. 

ISTT .EQ. 

NOTE (LIT) 

NOTE (LTT) 
BLOAD(LTT) 
CONTINUE 
IF ( HLOAD(LTT) 
GO TO 9130 
CONTINUE 
CONTINUE 
INPUT TABLE 5B 



FCB CONFLICT (SEE FOHBAT 130 ABOVE) 



DO 



IF 
IF 
IF 







GO 

GO 




TC 6000 
TC 6000 
) GO TC 



N2 
= 1 

= MSTIF (ISTT) 



5990 



EQ. HSTIF(ISTT) ) GO TO 6000 



04000 

04001 

04002 

04003 

04004 

04005 

04006 

04007 

04008 

04009 

04010 

04011 

04012 

04013 

04014 

04015 

04016 

04017 

04018 

04019 

04020 

04021 

04022 

04023 

04024 

04025 

04026 

04027 

04028**8 

04029**8 

04030*47 

04031**8 

04032*84 

04033*36 

04034*84 

04035*84 

04036*37 

04037*35 

04038**8 

04039**8 

04040**8 

04041**8 

04042**8 

04043**8 

04044**8 

04045**8 

04046**8 

04047**8 

04048*10 

04049*35 

04050*35 

04051*40 

04052*35 

04053*35 

04054*35 

04055*35 

04056*35 

04057*35 

04058*35 

04059*35 

04060*35 

04061*35 

04062*35 

04063*35 

04064*35 

04065*35 

04066*35 

04067*35 

04068*35 

04069*35 

04070*35 

04071*35 

04072*35 

04073 

04074 

04075*90 

04076*90 

04077*90 

04078 

04079 

04080 

04081 

04082 

04083 

04084 

04085 

04086 

04087 

04088 

04089 

04090 

04091 

04092 

04093 



261 



P£INT_8 
PEI 



J? 3 J!S3h-3i. ,j°Sa IfflV 31 - 0) 30 T0 6170 S5§|| 

GO TO 6900 P,f*92Z 

6170 CONTINUE 0J098 

PEIh"iJ BCD5B - NS - °> G ° T0 6200 04100 

PEINT 23 04101 

GO TO 6900 04102 

llll u twi*.-Vi& G0 TC 62S0 8J § 

"' U GO TO^T^ = ^ 8S 81 

o250 PRINT 17 04107 

6275 PHINT 41 04108 

PHINT 43 04109 

6300 CONTINUE 04110 

COHSENT - READ FIHSI CARD 01 TABLE 5B MUX 

&2>kD 42, NAT.NCDAT Ruiil 

NCDA(NAT) = NCDAT nuii» 

NPCTOT (NAT) = S! 5 

HCK5 = NCE5 + 1 %?,}}% 

PSINT 44, NAT,NCDA(NAT) n/iiiT 

IF (NAT .12, .OE. NAT . GT. HNCS) GO TO 8350 nuiin 

CO«.«, - II {SSTemHSeb 0° F 8 CA^S DAT - GT ' W^B 8780 

DO 6400 II = KNCDAT SS12? 

aEAD 45, NDIV(NAT.II) , BI(N AT.II) ,DI (N AT.II) .II (HAT III 0U199 

J I^«(NA| { li),Nls(NiT.if) J^kltii).E«(5lT^S), 0^11*48 

nce5 = ficpi + 1 niti 2 .** 48 

IF ( H3IVrNAT,II) . NE. ) GO TO 6320 naioA 



, IB INK, BI?NAT,II) , DI(NAI,II) . II (NAT. Ill IHF 



GO TO 5340"" iUMWfli, = "*WUTHSW) + 1 jJ1) 04129* 48 

b 340 COSTIOTB NPcicT < SAT 5 " BPCTCT(NAT) ♦ NDIV(NAT,II) U 1 J 5 * "* 8 

2 GO 55 a |9S ( 5 NAI ' II) * SE - 1 ' AND - IHECT(NAT,II) .HE. 0) §4137 

O400 CONilNui NAT,II) ' LE - ° -° E " » SS < !,AT 'II) -GT- MNSS) GO TO 8770 04139 

IF ( NPCTCT(NAT) . GT. HNPCS ) GO TO 9101 §4141 

6*00 llvWl •"• (NCD5A + NCD5B)) G0 T0 " 00 R4142 

COMMENT - INPUT TABLE 5C kUH 

PEINT 7 04144 

PEINT F 3(j NCr>5C ,GT ' ° '° E - KEEP5C ' GT - 0) GO TO 7200 04146 

GO TO 7500 04147 

7200 PEINtM NCD5C * NE ' °> GC T ° 725 ° 04149 

PHINT 23 0al50 

GO TO 7500 04151 

™ n wrs ~*u^ Q0 ic 728 ° nil 

27C GCTO730r SW -- 1 

7280 PRINT 17 9Slg§ 

7300 CONTINUE 9,V,V R 

IF (2L NC £ SIc2-= EC NcEI^ fi 2 ) G ° T ° 74 °° g| fh 7 

,- -, », IF (NCD5C2*2 .NE. NCD5C ) GO TO 8730 04161 

COflaEHT - INPdT STEESS-STEAIN CURVe'oK TSC CARDS 04162 

PEIMT°81 350 " = 1 ' NCI)5C2 04163 

2EAD l>! 2 ^^ L '| C i^ TI S|^ T » &1?H ' B2T «{ 8SI Id) .1=1,3). (NEPT (I), 1=1, 8) 04165 

N3IG(NC,lf o NSIT(I) 04167 

7310 CONTIN^'^ ""« 

SSJfif».-J3F | 

3ATfiL(iiC} ■ HTEL 0U177 

ALPHA (NC) = ALPH 04173 

BETA (NC) = BET 04174 

„ D * F i AI2L .NE. MTNO ) GO TO 7315 04175 

GO TO 7317 SC ' SETS ( Hfc ) ,ISS(NC), (NSIG(NC.I), I = 1,NPTT ) 04176 

7315 CONTINUE SJHI 

7317 ^ IK £ ^£ N j5| EL ' KC ' NFTS < NC >'I S S(NC), (NSIG(NC,I), I = 1 „ NPTT ) 04179 

fsj| .so, i .and. UZII1I .^."Sf^s-ft-aiM 1 ' NPTT > Bill 

$111 'I8* J * AKD - EEPT ' -KE- GO TO 8996 04183 

,|SJ| .HI, 1 .AND. ISJT .NE. 0) GO TO 8800 04184 

NPiT LT. 2 -OH. NPTT . GT. 3 GO TO 8790 04185 

(NC .II, .OH. NC , SI. MNSS) GO TO 8770 auiSA 

COKKENT - SUBROUTINE SECUH(NC) DEALS KITH STRESS-STRAIN rriPVF tcnMRPR nrnlip? 

COHHENI - AND ITS SD3 DIVISIONING FOE FUEPOSES OF INELASTIC TEEATMENT 04188 

CJMENI - FOE THE PRESENT INELASTIC CASE IS RESTRICTED TO SYMMETRIC 04189 




262 



£88818$ ~ P51?BS BITH^HUHBEfi OF INPUT POINTS (OF THE SYMMETRY PARTi 
COMMENJ - OEIGIN H |o,of Q T ° aSSINL ( " ** E ™« > INCIUDlk 

5|NT - 3U3R0UTINE SECUS ALSO DETERMINES THE IMPORTANT INFORMATIONS 



c 
c 
c 

COMMENT 

COB 

COB 

C 



8M3 



7320 

COMMENT 



IF (ISJT 
GC TO 7350 



.EQ. 1 .AND. NPTT 



.IE. aSSINL ) GO TO 7320 
CONTINUE 

coSSiSi - iSisi^IJS B a l|ggi2 TI " SECUE ?CE THE N0I)1I1,EAE ^stic 

DO 7330 I = 1,HNCS 

NAT = I 

NCDAT = NCDA (NAT) 
IF (NCDAT . EQ. -1) GO 10 7330 
DO 7325 ITE3P = 1, NCDAT 
II OJSSJKAT.ITEBP) .BE. NC) 
IF (NDlViNAT,IIEJlP) .20. 0) 
CAL1 „ „ SgcOR (NC,IABAN) ' 

GO TO 7350 



GO TO 7325 
GO TO 732 5 



7325 
7330 
7350 

7400 



CONTINUE 
CONTINUE 
CONTINUE 
GO TO 7500 
CONTINUE 

NCD5C3 
IF (NCD5C3*3 



NCD5C/3 

. BE. NCD5C ) GO TO 
COMMENT - INPUT FLEXURAL STRESS-STRAIN CURVE 
DO 7450 II = 1,NCD5C3 
PRINT 61 



9240 

AND 



SHEAR DATA IN 3 CARDS 



READ 



04192 

04193 

04194 

04195 

04196 

04197 

04198 

04199 

04200*86 

04201*86 

04202*86 

04203*86 

04204*86 

04205*86 

04206*86 

04207*86 

04208*86 

04209*86 

04210*86 

04211*86 

04212*86 

04213*86 

04214*52 

04215*52 

04216*47 

04217*47 

04218*47 

04219*47 

04220*47 

04221*47 



7410 



DO 2 74^0 L 'l C = N 1 TT NPTT T ' ALPH ' BEI ' (NSIT(I) ' I=1 ' 8) ' (NEPT(I) ' I=1 ' 8)5(i 222*47 

NSIG(NC,lf = NSIT(I) 04223*47 

N2PS{NC,I) = NEPT(I) 
CONTINUE 

NPT3 (NC) = NPTT 

ISS(NC) = ISJT 

EATfiL/NC) ■ HTRL 

ALPHA (NC) = ALPH 

BETA (NC) = BET 

STRI .BE. MTNO ) GO TO 7415 
(NC), 



KC, NETS. 



I? ( 
PRINT 87, 
„„.„ GO TO 7417 
7415 CONTINUE 
7417 ""^^"'".HMCrcj.ISSCIC, 

FEINT 34, 
BEAD 201,GS(NC) 
PRINT 241 
PRINT 201, GS (SC) 
IF (ISJT .EQ. 



ISS(NC), (NSIG(NC,I), I = 1,NPTT ) 



(NSIG(NC,I), I = 1,NPTT ) 
(SEPS(NC,I), I = 1,NPTT ) 



COMMENT 
COHHENT 
COMMENT 

C&fliiENT 
COHHENT 
COMMENT 
COMMENT 
COHHENT 
COMMENT 



IF 

IF 

IF 

IF 

SUB 

AND 

FOR 



ISJT ,Eu. 
'ISJT .SB. 
NPTT .IT 
NC .11.0 



1 
1 
1 
2 
.OR 



.AND. 

.AND. 

-AND. 

.OR. 

NC 



:(1) .NE. 0) GC 
:(1) . NE. 0) GO 
: .NE. 0) GO TO 



NSIT 
NEPT 
ISJT 
NPTT .GT 
GT. BNSS) 



8 

GO 



TO 8996 
TC 8996 
GO TO 8800 
GO TO 8790 
TO 8770 



04224*47 
04225*47 
04226*47 
04227*47 
04228*47 
04229*47 
04230*47 
04231*47 
04232*47 
04233*47 
04234*47 
04235*47 
04236*47 
04237*47 
04238*47 
04239*51 
04240*47 
04241*51 
04242*47 
04243*47 
04244*47 
04245*47 
04246*47 



lOUTINE SECUR(NC) DEAIS KITH STRESS-STRAIN CURVE NUMBER NC04247*78 



ITS SUBDIVISICNING FOP. PURPOSES OF INELASTIC TREATMENT 
THE PRESENT INELASTIC CASE IS RESTRICTED TC STMHETRIC 
CURVES KITH NUMBER OF INPUT POINTS (OF THE SYMMETRY PAET) 
LESS THAN OR EQUAL TO MSSIHL ( = 4 AT PRESENT ) INCLUDING 
ORIGIN (0,0) 
INI 



SUBROUTINE SECUE ALSO DETERMINES THE IMPORTANT INFORMATIONS 
FROM THE SPECIAL INPUT CURVE FOR MUD STEEL ( WITH VIRGIN 
STRAIN HARDENING ) 
IF (ISJT .EQ. 1 .AND. 
GC TO 7450 



NPTT .IE. MSSINL ) GO TO 7420 



7420 CONTINUE 
COMMENT - SKIP CALLING SUBROUTINE SECUR FOR THE NONLINEAR ELASTIC 
COMMENT - STRESS-STRAIN MODEL 
DO 7430 I = 1,MNCS 
NAT = I 

NCDAT = NCDA (NAT) 
(NCDAT .EQ. -1) GO TC 7430 
7425 ITEM? = 1, NCDAT 

(NSS (NAT.ITEMPf .NE. NC) GO TO 7425 
(NDIVJNAT,ITEMP) . EQ. GC TO 7425 
CALL SHCUR (NC,IABAN) 



IF 
DC 
IF 
IF 



7425 

7430 

7450 

7500 

COMMENT 



7700 



7750 
7770 



GC TO 7450 

CONTINUE 

CONTINUE 

CONTINUE 

CONTINUE 

INPUT TABLE 5D 
PRINT 6 

IF (HCD5D .GT. .OS. X2EP5D .GT, 0) GO TO 7700 
PRINT 30 

GO TO 8000 

IF (NCD5D . NE. 0) GO TO 7750 
FEINT 17 
PRINT 23 

GO TO 8000 

IF (KEEP5L .EQ. 1) GO TC 7780 

DO 7770 I = T,MNQW 
NPTH (I) = -1 



ta 



04248*78 

04249*78 

04250*78 

04251*78 

04252*78 

04253*78 

04254*78 

04255*78 

04256*78 

04257*78 

04258*86 

04259*86 

04260*86 

04261*86 

04262*86 

04263*86 

04264*86 

04265*86 

04266*86 

04267*86 

04268*86 

04269*86 

04270*86 

04271*86 

04272*53 

04273 

04274 

04275 

04276 

04277 

04278 

04279 

04280 

04281 

04282 

04283 

04284 

04285 



263 



GO TO 7800 
7780 PRINT 17 
7800 CONTINUE 

PRINT 88 

NCD5D2 = NCD5D/2 
IF (NCD5D2*2 .HE. I1CD5D ) GO TO 3730 
COMMENT - INPOT HEKBEE Q-H CURVE Cn' TSC CARDS 
m DO 7350 II = 1,NCD5D2 
BEAD 89 
DO 

NQM(NC,I) '= NQHTU) 
N*M(NC,I) = NliflT(I) 
CONTINUE 

NPTM (NC) = NPTT 
ISM (NCI = ISJT 
PKINT 85, NC,NPTM(NC) ,ISM(NC) L jNQH(NC,I), I 



%\m 



7810'Ti'"NpfT ( * ' 



7810 



BXHX B3, NC,NPTM(NC) ,ISM(NC) , ( 
HINT 86. (Niii(NC,I), I » 1.NPTT 
IP (ISJT .EQ. 1 .AND, NQMIM 



7850 

8000 
COMMENT 
COMMENT 



(ISJT .3Q. 
[ISJT .HE. 

NPTT .LI. 

NC ,LI.O 



TT) 

'.I 



1 -AND. NSBT 

1 .AND. ISJT ".HE 

2 .08. NPTT .GT. 



Cti 



11 



0) GC TO 8996 
0) GO TO 8996 
GO TO 8800 
GO TO 8790 
.OR. NC .GT. HNQHH) GO TO 8750 

CONTINUE 

CHECK FOE INCOMPATIBLE DATA 
CURVES ON SAME MEMBER 
DO 8100 I = 1.NST 
ISTT = I ' 
(INLOP (ISTT) . EQ. 
NALT = NAL(ISTT) 
NAHT = NAR(ISTT) 
NCDA(NALT) .EQ. -1) GO 10 8900 
aiCDA(NART) .EQ. -1) GO TO 8910 
NCDA(NALT) .NE. NCEA(NABT)) GC TO 8920 
NCDAT = ilCEA(NALT) " 



04288 
04289 
04290 
04291 
04292 
04293 
I = 1,11) 04294 
04295 
04296 
04297 
04298 
04299 
04300 
= 1,NPTT) 04301 

04302 
04303 
04304 
04305 
04306 
04307 
04308 
04309 
CROSS-SECTION AND STRESS-STRAIN0431 

04311 



NE. 

NE. 



IF 



IF 
IF 
IF 



0) GO TO 8100 



1, NCDAT 



GO TO 
GO TC 



3030 



8040 

COMMENT 
COMMENT 



DO 8050 K = 
KJ = K 

NSSL1 = NSS(NALT,K 

NSSET = NSSfNAfil.K 

(NPTS(NSSLI) .EQ, ^1 

(NPTSJNSSRT) . EQ. -1 

NPTSJNSSLT) .NE. NP„ 
(IRECT (NAIT.K) . NE. IBECTf 
NPTT = NPTS(NSSLl) 
DO 8030 KK = 2, NPTT 
GO ^H|NALT,K)*(NEPS(NSSLT,KK) 

CONTINUE 

NPTT = NPTS(NSSHI) 
«" 8040 KK = 2,NPTT ' 



IF 
IF 
IF 
IF 



8930 

8940 



SiNSSRT}) GO TO 8950 

" NAKT.K)) GO TO 8960 



NEPS (NSSLT,KK 



1)) .IE. 



GO |§ fl ^^f I ' K )*< NBPS ( !,s SHl,KK) - NEPS(NSSRT,KK 

CONTINUE 

H» ( 22jyi N ^ LT ' K I - EC > .AND. NDIV(NAHT,K) . EQ. 0) GO TO 8050 
THE fOLLdHING F&UR CHECKS APPLY ONII FOR THE INELASTIC 



STRESS-STRAIN CASE 
IF ( KDIVj[NALT,K) . NE. 
N3SLT 



8050 
81C0 

COMMENT - 



IF 

IF 

IF 

CONTINUE 

CONTINUE 

IF ( NCD5E 



SM(NALT,K) 
EM(NALT,K) 



. EQ. 



. NE. 

NE. 

, NE. 



NDIYfNART, K) 
NSSRT ) 
SM(NART,K) ) 
EM(NART,K) ) 



GO 


TC 


9103 


GO 


TC 


9104 


GO 


TO 


9105 


GC 


TO 


9106 



dt 



CHECK FOE COMPLIANCE HITH THE SPECIA 
COMMENT - PLACED ON SIGKA-EPSILC N CURVES FOE THE -INELASTIC' CASE 
ill) o IU4 I = IjMNCS 
NAT = I 

NCDAT = NCDA (NAT) 
(NCDAT .EC. -1 ) GC TO 8104 
8102 II = 1, NCDAT 
( NDIV(NAT,II) _EQ 
NC = NSS(NAT,II) 
ISJT = ISS(NC) 
NPTT = NPTS(NC) 
ISJT .NE. 1 ) GC TC 9107 
NPTT .GT. MSSINL ) GO TO 9109 



04312 
04313 
04314 
04315 
04316 
04317 
04318 
04319 
04320 
04321 
04322 
04323 
04324 
04325 
04326 
04327 
04328 
04329 
04330 
1)) .LE. 0.0)04331 
04332 
04333 

mn 

0.0) 04336 
04337 
04338 
04339 
04340 
04341 
04342 
04343 
04344 
04345 
04346 
04347 
04348 



IF 
DO 
IF 



) GC TO 8102 



IF 
IF 
8102 CCKTINU_ 
8104 CONTINUE 
83104 
COMMENT 



IF 



GO 



ISTT = I 
(INLOP (ISTT) 
K = 1 
NSLT = 
NSRT = 
- TO 8120 
8105 K = 2 

NSLT = 
NSEI = 
GC TO 8120 
8110 K = 3 

USLT = 
NSHT = 
3120 CONTINUE 

IF (NSLT .EQ. 



NSXL(ISTT) 
NSZfi(ISTT) 



NSYL(ISTT) 
NSYR(ISIT) 



NSZL(ISTT) 
HSZR(ISTX) 



OE. NCD5C . EQ. _0 I GC TO 88104 

(TEMPORARY) RESTRICT IONS04349 

04350 
04351 
04352 
04353 
04354 
04355 
04356 
04357 
04358 
04359 
04360 
04361 
04362 
04363 
04364 
04365 
04366 
04367 
04368 
04369 
04370 
04371 
04372 
04373 
04374 
04375 
04376 
04377 
04378 
04379 
04380 
04381 



CONTINUE 

CHECK^OB^INCOMPATIBLE DATA ON MEMBER Q-H CURVES 



EQ. 0) GO TO 82C0 



AND. NSflT .NE. 0) GO TO 8993 



264 



B IIP i*i2*J ° } .*8? -1 > WlO 899 i 89183* w 

IF (NPTH/nSHTS .15, -1 GO TO 8992 8#1§I 

If (NPT«lN3I.TJ .Hi. uiklHSET) TO 8993 ggllS 

Rm NPTT = NPTM(NSLT) ' nzf3pf 

DO 8160 U = 2.NPTT 8#lf§ 

2 GO ^ M H!fJ*<sSH(NSLT f II) - Ntf«( N SLT,II- 1), . 1E . . 0) otlU 

3160 CONTINUE 04389 

DO 817^11 STJSIF' 8«1? 

2 GO ^ a |iffJ*(SfifJ(N S aT,U) - HHHCHSBT.II - 1)) mUm 0.0) SSJll 
8170 CONTINOE 04394 

8175 CONTINUE 04395 

8200 C 3 §N?2 N! }i 105 ' 8110 ' 82C0 >'* 83«7* M 

GO TO 9900 2?I2§ 

8300 PRINT 30 04399 

GO TO 9700 04400 

8310 PEINT 31 04401 

GO TO 9700 04402 

8320 PRINT 32 04403 

GO TO 9700 04404 

8330 PRINT 33 04405 

GO TO 9700 04406 

8340 PRINT 34 04407 

GO TO 9700 04408 

3350 PRINT 35 04409 

GO TO 9700 04410 

8510 PRINT 51 04411 

GO TO 9700 04412 

8520 PRINT 52 04413 

GO TO 9700 04414 

8530 PRINT 53 04415 

GO TO 9700 04416 

8540 PRINT 54 04417 

GG TO 9700 0441 8 

6550 PKINT 55 04419 

30 TO 9700 04420 

8560 PRINT 56 04421 

GO TO 9700 04422 

8570 PEINT 57 04423 

GO TO 9700 04424 

8530 PRINT 53 04425 

GO TO 9700 04426 

3610 PRINT 61 04427 

GO TO 9700 04428 

8650 PRINT 65 ° 44 29 

aari „ GO TO 9700 8IS-I9 

86b0 PRINT 60 g*f*3j 

GO TO 9700 n«,,ll 

3670 PRINT 67 04433 

„„.„ GO TO 9700 ftflSlS 

8710 PRINT 71 SSSli 

GO TO 9700 huStt 

3720 PEINT 72 04437 

GO TO 9700 m.iAo 

8730 PRINT 73 g»«9 

„_ , GO TO 9700 nXSSi 

8740 PRINT 74 8?2*1 

GO TO 9700 SJiSSi 

8750 PEINT 75 §^444 

,.,,„ GO TO 9700 fibttSS 

8760 PRINT 76 Xuu^I 

„_„„ GC TO 9700 nSSSI 

3770 PRINT 77 ofittttB 

GO TO 9700 S5!S q 8 

3780 PRINT 78 nH^n 

,„„„ GO TO 9700 nltSi i 

8790 PRINT 79 SfgiJ 

GO TO 9700 HttStl 

8800 PRINT 80 8*til 

GO TO 9700 nLult 

8900 PRINT 90, NAL1 2Hf§ 

GO TO 9700 nu2^7 

8910 PRINT 90, NAR1 na/ffn 

GO TO 9700 nSSIg 

8920 PRINT 92, KUJ, NART, ISTT Ottttfo 

GO TO 9700 S!??S 

B930 PRINT 93, NSS1T niltl 

GO TO 9700 nn/ii^ 

8940 PRINT 93, NSSBT naul/< 

GO TO 9700 04464 

8950 PAINTS, NSSLT, NSSRT,KJ, SALT, NART, ISTT §4466 

3960 PRINT o 9|,K^ o NALT, NART, ISTT jjjjjj 



3991 PRINT 991, NSIT 0U(1 -7n 

GO TO 9700 SuS-71 

8992 PEINT 99 1, NSET nuul-i 

GO TO 9700 ntm 

8993 PRINT o 993, y N3II, NSRT, ISTT g^ 

8994 PRINT 994, N3SLT,KJ r NALT, ISTT gjj^f 

° u iu " uu 04477 



265 



8995 

8996 

8997 

8998 

9101 

9103 

9104 

9105 

9106 

9107 

9109 

9120 

9130 

9220 

3230 

9240 
9700 
9900 



PEIN G0 9 TO'9700 ST ' KJ ' KART ' ISTT 

PRINT 996 

GO TO 9700 
PRINT 997, NSLT.ISTT 

GO TO 9700 
PRIST 997, NSET,ISTT 



rnx a a as / , 
GO TO 9700 
PRINT 101, 
GO TO 9700 
PRINT 103, 
GO TO 9700 
PRINT 104, 
GO TO 9700 



NAT, MNPCS 

ISTT, 

IS1T,K 



K 



C 

c 

c 
c 
c 
c 
c 
c 



:cmment 



PRINT 105, ISTT.K 

GO TO 9 700 

PRINT 105. ISTT.K 

GO TO 9700 

PRINT 107. NAT, II, NC 

GO TO 970fi ' 

PfiIK L 109,NAT.II,NC,flSSINI 

GO TO 9700 
PRINT 120, 2NE 

GO TO 9700 
PRIST 130, LIS 

GO TO 9700 
PRINT 2 20 

GO TO 9700 
PRINT 230 

GO TO 9700 
PRINT 240 

IABAN = 1 

CONTINUE 

NSIL = NS1 

IF ( IABAK 



-..-..,. .SO. 1 ) GO TO 13000 

IDENTIFY . THE.VAEIOllS CATEGORIES OF STIFFNESS TYPES AS 



MODEL 



J: 



-> 



-2 
-1 


1 
2 



LINEAR 

NONLINEAR ELASTIC 

MA SING ALPHA= 

BASING + DEGRADATION ALPHAS 

YBRID CR0i L iE^I§', D Mf|i E H E ^ P I fi0 ^E£ si™ 

cicfi fl Ii^xci Tffi aiGHEST AH °^ thepoIIiblFtypII fob 

DO 12000 I » 1-HST 

ISTT =1 

MODEL (ISTT) = -2 
IF ( INLOP(ISTT) . EQ. ) GO TO 12000 

NAT = NALJISTT) 

NCDAT = NCDA(NAT) 
MODEL (ISTT) = -1 



DO 



11000 



NTEBE 
TEMPA 
TEBPB 
11000 K 
NC 

NTEHP 
TEMPA 
THMPB 
CONTINUE 
IF ( NTEBP 
IF ' 





0.0 

0.0 

= 1. NCDAT 



&1ILU1U 
SS (NAT.K) 
NTEBP * NDIV(NAT.K) 



TEHP4 
TEMPA 



ALFH 
EETA 






.EQ. 



( IEMPA+TEMPE 
MODEL(ISTT) 
GO TO 12000 
11200 CONTINUE 

IF ( TEMPB .GI» 
MODEL(ISTT) 
GO TO 12000 
11400 CONTINUE 

IF ( TEMPA . GI. 
IABAN •= 1 
PRINT 140, IS1T 
GO TO 12000 
11600 CONTIN0E 

MODEL (ISTT) 
12000 CONTINUE 
13000 CONTINUE 
RETURN 
END 



• GT. 

= 



GO TO 12000 
1.0D-15) GO 



TO 11200 



1.0D-10 ) GO TO 11400 
= 1 



1 .0D-10 ) GO TO 11600 



04478 
04479 
04480 
04481 
04482 
04483 
04484 
04485 
04486 
04487 
04488 
04489 
04490 
04491 
04492 
04493 
04494 
04495 
04496 
04497 
04498 
04499 
04500 
04501 
04502 
04503*35 
04504*35 
04505*35 
04506*35 
04507*47 
04508*47 
04509 
04510 
04511 
04512 
FOLLOW 04513 
04514 
04515 
0,BETA=004516 
0,BETA=004517 
0,BETA#004518 
04519 
THAT 04520 
04521 
04522 
04523 
04524 
04525 

838* 

04528 
04529 
04530 
04531 
04532 
04533 
04534 
04535 
04536 
04537 
04538 
04539 
04540 
04541 
04542 
04543 
04544 
04545 
04546 
04547 
04548 
04549 
04550 
04551 
04552 
04553 
04554 
04555 
04556 



*** 

COM2 
COMM 
COMM 
COMB 
COBB 
COMM 
COiifl 
COHH 

coafl 

COBB 
COBB 



*** 

S 
ENT 
ENT 

ENT 
ENT 
ENT 
ENT 
ENT 
EN1 
ENT 
ENI 
ENT 



************ 
DBKOUTIHE SE 

- SOBROUTIN 

- BASIC INP 

- (FOR THE 

- USED, TOG 

- DEGRADATI 

- PROPER SC 

- THREE TIP 

- MA5ING HO 

- MASING ffl 

- SPECIAL F 

- FOR THE P 



************** 

CUR ( NC. IABA 
i. SECUH DEALS 
OT INTEGER CUR 
SPECIAL CASE 
ETHER KITH THE 
CN, AND YIELD 
ALE FACTORS AE 
ES OF TNELASTI 
DEL 

IH DEGRADATION 
OH MILD STEEL 
RESir;NT, IN EL AS 



** SUBROUTINE ********************* 



KITH T 




ECOBPOSITION OF THE 

NC . 

EL, ONLY ONE COMPONENT IS 

OF VIRGIN STRAIN HAHDENIN 

RE OF IN SUBROUTINE FAE2 

TRAIN CURVES ARE POSSIBLE 

PHA = , BETA = 

PHA * , BETA = 

PHA * , BETA * i 

S RESTRICTED TO SYMMETRIC 



************ 

04557 

04558 

04559 

04560*90 
G 04561*90 

04562*90 

04563 

04564 

04565 

04566 

04567 

04568 



EV 



266 



Eypriiyt^zigteBiiPaiieH wgp less than oe eqoal to nm 

S|SC|SDIHe BRANCHES ABE NOT COSSIdIeED AND HENCE MUST NOT 04571 



c 
c 

COMMENT 

C BE INPUT 

COMMENT - NO LIMIT IS PUT ON MAXIMUM STBAIN 

IMPLICIT REAL ■* ■ 

DI 

COH 
2 



PLICIT REAL * 8 (A-H , O-Z) 
KENSION QQM1), WSM1)' 2MAXM0) 
HKON /BLOCi3/ NPISf OBJ, ISS( 08), N„, 
NSITM1) ' NEPT(II) 
COMMON /SKT12/ EPSIEI (0 8,03), SIGMAX (08 ,03) 
COMHON /SKT31^ ALPHA (6) , *Bjf A ''(8), SMLSLP (8) , 



SIG(08,11) ,NEPS (08,11), 



Hi: 



HATHL 



HI 



EPSTKD(8) , 



SLOPHD (8) , SIGULTl 
2 FORMAT ( 10X, 4 ( F11.4, 4X ) ) 
9 FORMAT ( / ) ' 

90 FORMAT (10X,37HDETAIL5 OF BASIC STRESS-STRAIN CURVES,/, 10X, 
24HSCALING FACTORS EXCLUCED,/) 



04572 
04573 
04574 
04575 
04576 
04577 
04578 
04579 
04580 
04581 
04582 
04583 
04584 



100 FORMAT (10X,14HCUBVE NUMBER = ,14, 5X ,25h'"# OF COMPONENT SPRINGS =, 04585 



2 14) 
102 FORMAT (10i 



2 F 13HBAX ( STR£s^OF S / EAINS ' 6X ' 9H STEESSES ' 6X ' 12HSTIFFNESS CF,3X, 



04586 
04587 
04588 
04589 
04590 
04591 
04592 




122. FORMAT (//,33R EREOHIN INPUl'OF SIG-EP 'CURVE #Cl3,/, 
m DSGSADATIOS^ALGOEITKM .(ALPHA _*_0]l DEFINED (5iILX IF 

'iS PEHHITTED, 04609 



)) 

?T FOR "MILD") ) 



2 5yH DEGRADATION ALGORITHM (... 

J 20H CONTINUOUSLY CONVEX-/, 20H (EXCEPi run -ai 
124 FORMAT 4//,25H **♦* BARKING FOR ^CUEVE *,I3,5H ****,/, 

2 61H HAblNS MODEL WITH CURVE NOT CONTINUOUS!! CONVEX 

3 14H AT USEES RISK ' 
126 FORMAT 



04597 
04598 
04599 
04600 
04601 
04602 
04603 
04604 
04605 
CURVE IS, 04606 
04607 
04608 



2 40fl 4 
130 FORMAT 
132 FORMAT 
134 FORMAT 
136 FORMAT 

138, FORMAT 



180 



: USEES RISK ) 
(//,33B ERROR IN INPUT OF SIG-EP CURVE *,I3,/, 
POINTS MUST BE USED FOR "MILD" CURVE ) 
{//,5X,28E ALPHA MUSI BE BETWEEN 5 1) 
//, 5X,34H****SAENING : ALPHA SEEMS HIGH****,//) 
(//,5X,18H BETA MUST BE > ) 
(//, 5X,37H***HABNING : BETA SI 



190 



04610 
0461 1 
04612 
04613 

04614 

BETA SEEMS VERI HIGH****,//) 04616 

NAGAIN =0 / 

CONTINUE 

NPT = NPTS(NC) 
DO 190 J = 1,NPT 

QQ (J) = NSIG 

-« (J) = 



WW (J) = NEPS 
CONTINUE 

NPTB2 = NPT - 2 
NPTM1 = NPT - 1 



(NC,J) 
(NC,J) 



GO TO 2 05 



IF ( NPTM2 -SO. ) 
DO 200 J = 1,NPTM2 

SLOK= ( CQ (J + 1 )-QQ (J) ) / («K (J + 1 ) - jjjj (J) ) 

STF =IlCK - Bl§rtl +1),/ ' WB(i + 2) H " (J 



♦D) 



RMAX (J) = WW (J + 1) 

200 CONTINUE 
205 CONTINUE 



* STF 



IF 
IF 



ialx(NPiMl>= ^S|f);Cg|{"">»/("(»")-»(»WHi) 

' (NC) -EQ. 

(NC) ,LT. 
tf = 1 



ILE ) GO TO 400 
1.0D-10) GO TC 300 



5ATEL(NC 
BETA 
IA6AN' 
PRINT 120, NC 
GO TO 1000 
300 CONTINUE 

DO 350 J = 1.NPTM1 

IF ( EM AX (J) -GE. 0-0 ) GO TO 350 
GO TO 370 
350 CONTINUE 

GO TO 390 
370 CONTINUE 

IF ( ALPHA (NC) 
IABAN = 1 
PRINT 122, NC 
GO TO 1000 
380 CONTINUE 

PRINT 124, NC 
390 CONTINUE 

SMLSLP (NC) = 
EPSTHD(NC) = 
SLGPHD(NC) = 
SIGULT(NC) = 
GO TO 500 
400 CONTINUE 

IF ( NPT -EQ. 4 ) 



LT. 1.0D-10 ) GO TO 380 



WK(2) 



0.0 

10000.0 
0.0 
CC(NPT) 


* 


GC TO 410 



!7 
18 
04619 
04620 
04621 
04622 
04623 
04624 
04625 
04626 
04627 
04628 
04629 
04630 
04631 
04632 
04633 
04634 
04635 
04636 
04637 
04638 
04639 
04640 
04641 
04642 
04643 
04644 
04645 
04646 
04647 
04648 
04649 
04650 
04651 
04652 
04653 
04654 
04655 
04656 
04657 
04658 
04659 
04660 
04661 
04662 
04663 
04664 



267 



IF ( NAGAIN .EQ, 
IABAh = 1 
P8INT 126, NC 
GO TO 1000 
41 CONTINUE 

NTEHPA = 1 

STEHEB = 1 

IF ( ALPHA (NC) 

ccasEiiT - if Alpha is hot 

ALPHA (NC) 
NTEBEA = 
CONilNHE 



1 ) GO TO 500 



. GT. 1. OD-10 ) GO TO 420 
INPUT FCS MILD(STEEL), OSE 

= V a 1 



420 

COMMENT - IF b'ETA 



IF (BETA (NC) -GT. 1. OD-10 ) GO TO 440 
IF BETA IS NOT INPUT FOB MILD (STEEL) 
COMMENT - AS ZERO. HOHEVEB IT IS COTPUT UNDER THE" •"COHPUTED • "TITLE 



(STEEL) , THEN IT IS TAKEN 



440 



500 



betaTnc) = o 

NTEBEB = 
CONTINUE 

SHLSLP(NC) 
EPSTHD (NC) 
SLOPHD (NC) 
SIGOLT (NC) 
NPTS (NC) 
NAGAIN = 1 

GO TO 180 
CONTINUE 
PEINT 9 
PEINT 90 

PEINT 100, NC, NPTM1 
PEINT 9 
P5INT 102 

PEINT 2, KS(1), QQ(1) 
DO §00 J = 2,NPT 



KH^/ 3) " QC(2) ] ' ( B »(3)-»H(2) ) 
iJQW ,> ~ eC(3) ' / ( %V <*)•« ( 3 ) ) 



800 



STF = HKAX(J-I) / (jg (J) 

P£IH CONTINtJE J) ' CC(J) ' "** E " A ^ J - 1 ) 
DO ^900 J = 1,EPTM1 



COBMENT - o^IOJ^j. 1« SIMlIgC.J^PpiAI. TO 



900 



EPSIEL NC.J = WHfJ+1) 
SIGBAX NC,J) = EBAX(J) 
CONTINUE l ' 



NC 



950 



IF l MATEL (KC) . EQ. HILD ) GO TO 950 
.103, ALPHA (SC), BETA(NC) 
9 82 

PlilHT 104 



PEINT 103, ALPHA (N< 
GO TO 982 
CONTINUE 



PE 



IF ( NTEBEA + NTEHPB . EQ. ) 

IF ( NTEKPA .EQ. .AND. NTEHPB . If. ) GO 

IF LNTEEPA .HE. .AND. NTFKPB . EQ . ) GO 

INT 135, AL.PHA (NC), BETA (NC) ,SBLSLP(NC), EPSTHD 



04665 
04666 
04667 
04668 
04669 
04670 
04671 
04672 
A SEASONABLE VALUE 04673 
04674 
04675 
04676 
04677 
04678 
04679 
04680 
04681 
046i82 
04683 
04684 
04685 
04686 
04687 
04688 
04689 
04690 
04691 
04692 
04693 
04694 
04695 
04696 
04697 
04698 
04699 
04700 
04701 
04702 
04703 
04704 
04705 
04706 
04707 
04708 
04709 
04710 
04711 
04712 



GO TO 980 



GO TO 970 

~ TO 960 
(NC) , SLOPHD (NC) , 



96 



SIGU"lt"(NC) 
GO TC 982 
J^PSINT 106, ALPHAJNCKBETA(NC) ,SHLSLP( NC) , EPSTHD (NC) ,SLOPHD(NC), 

GO TO 982 
970 2 PKINT 107, |LPUAJI1CK , BETA (NC) , SKLSLP (NC) , EPSTHD (NC) ,SLOPHD(NC) , 

GO TO 982 
980^PHIi;T 108, ALPHA (NC), BETA (NC) ,SBLSLP( NC) , EPSTHD (NC) ,SLOPHD(NC), 

A bx GJ LT ( NC) 

982 



984 



985 



936 



987 



1000 



SIGULT | 
CONTINUE 
IF ( ALPHA(NC) .GE. 
IABAN = 1 
PEINT 130 

GO TO 1000 
CONTINUE 



0.0 .AND. ALPHA (NC) . LE. 1,0 ) GO TO 984 



PS 



IF ( SSATEL(KC) -HE. MILE ) GC TO 9 
IF j ALPHA (NC) .LT. 0.35) GO TO 98 



985 
5 



CONTINUE 

IF ( BETA(HC) .GE. 0.0) GO TO 98 6 
IABAN = 1 
FEINT 134 

GO TO 1000 

CONTINUE 

IF f SATHL(NC) ,NE. MILE ) GO TO 987 

IF J BETA (NC) .IE. 0. 8 ) GO TO 987 
PEINT 136 

CONTINUE 

IF ( SMLSLP(NC) .GE, 0.0 ) GO TO 1000 
IABAN = 1 
PEINT 138 

CONTINUE 
RETURN 
END 



04713 

04714 

04715 

04716 

04717 

04718 

04719 

04720 

04721 

04722 

04723 

04724 

04725 

04726 

04727 

04728 

04729 

04730 

04731 

04732 

04733 

04734 

04735 

04736 

04737 

04738 

04739 

04740 

04741 

04742 

04743 

04744 

04745 

04746 

04747 

04748 

04749 

04 75 



********************************** SUBROUTINE ********************************* 

SUBROUTINE RDflLD 04751 

S 252183! " lUBBODTINE EDMLD INPUTS MEMBER LOAD DATA (TABLE 6) CHECKS 04752 

COMMENT - FOE BAD DATA. CCNVSfiTS IOADS AND DISTANCES TO MEMBEB 04753 

COMMENT - COORDINATES AND ECHO PKINTS DATA 04754 

IMPLICIT H£AL*H (A-E,0-Z) 04755 



268 

2 coa t^MY o/ ihkkm XfiL ( 75) - qxl ( 75 > * aYL < 75 > • gSIII 

3 KEEP5B,KEEP5C,KEEF5D,KEEP6, KEEP7, NCD2. NCD3A. 0476^*61 

4 HCD3B, NCD4A, NCD4B, NCD4c! NCD5a! NCD5B NCD5C 047fitt*£i 

5 NCD5D, NCD6 ' NCD7, IP8, 129. IP10 ' ITYPe' nu7fi£*£i 

2 cM 8wWk. B fiiipgiaI 1 bJII* B ^ 3fe ** ffi *'» 5 fe 6 »«*"™. °™* 61 

COHHON /Bits/ NLt£ ' HNJST ' BSJSS MS* 79 

COHMON / BR / PCBML, PCBJL, NLB, HLBA nfc77? 

9 PPR^T < SKX ^<; HSTl|(25),,KLOAD?25t7 «0DEL(25) §4772 

n £S52 A £ (, "°,H TABLE 6 - HEHBEE LOAD DATA ///) ntnni 

V° i9iI l U |i PROBLE^ ^VfSrafS B|*M|CSNTAG| OVE^LAST, 88?t1 

^ 1UB PROBLEM ,//,5X,15H LOAD PERCENT ,/,5X, 04775 



10 
3 



1| HUB f If: B: 2 "- Hi?:!: ls -iSIVTf '"' M 



14 FOBKAT |//,|0H ' LOAD UNiFOB« ^6 S ifg B a "NO AXIS , 04779 
| /'/) Q Q CAEDS OPT ' 04780 

15 FOBKAT (10X,5£10.3,19X,,A1) Sft 7 ^} 
5 FORMAT 5X,5E11.3;14X'A1[ 88213 

I7FOM1I J 48* the Mionfe DATA FROM THE PBEVIOUS PEOBLEM PLUS, 8J?I| 

18 FOfiflAT (//»20H LOAD TYPE .I5.6H CONTD,/,2X, 04786 

3 30fi QZ f ° Qi QY ' °*™1 

21 roaaAT r 5x,i5,eio,3,A4,ai) XS4S4 

^2 fOiHAT 51-15, £11. 3:u;a«'a1) 0479^ 

23 FOEHAT { TOE NONE ) OUTQU 

24 JOHJAl ( 20 ti NO DATA ) 8S222 
5^ |°|KfT 50B LOAD SPECIFIED BEYOND THE END CF MEMEEB ) 04796 
?-}. ?9? fl AT I 5 OH LOAD SEQUENCE MUST BE LONGER THIS 1/S tSSJtl na4o7 



?i |2f3 A l J ??g 10AD SEQUENCE HOST BE LONGEE THAN 1/H *SPAN 04797 

54 FOHHAT ( 51H LOAD SPECIFIED AT NEGATIVE DISTANCE ALONG MFMftl 0U7qfi 

55 o P £iI A 2,J 49H T0 DISTANCE CF ZEBO IMPLIES THAT IT IS FIRST . 04799 

3 20H DISTANCE™? ZERO SE0 - UENCE AJ,D NEXT CAED WILL BA7E fIoH.a' 04800 

5b 2 F ° aMT ( l^LCAD TYP^fol S S I!ci!lIg 31 TJBLE 6 BEiD B °* A " • J8f jjj 

57 3 FOR H AT ( 8§| ?O^I^ CO rllh A r "bWII^IoWUIV^ , 8*g8g 

2 10h SPECIFIED) 04806 

58 FCEHAT ( 51H ALL LOAD TYPES SPECIFIED BUT ALL CADS NOT BEAD 04807 

cq 2 „„-u^' , ?,%% CHECK CAED COUNT AND NUMBEfi OF LOAD TYPES) 04808 

52 l?M$'I ^9 H AXIS OPTION MUST BE 1,2.3, OB 4 I ' 04809 

°9 !8!S A £ | 5|fl NUHBEB OB CAECS TO FOLLOW HUST NOT BE NEGATIVE) 0481 

61 FCBMAT [ 48H CONCENTBATED LOADS AT 0.0 ABE NOT PEF.HITTED) 04811 

H ISI2 A 2 ( ?9 H LOADS CAN NOT BE INCREASED IF NO LOADS HELD ) 04812 

S§ 19SMZ I ^ ti L0AD TXPES HOST BE IN ASCENDING CEDEB ) 04813 

67 2 FOE, ] AT I 50H vAio£ IF a 2ND CAEgJSED FOB LOAD TYPE. DNIFCR« Ud , 04814 

71 FGSKAT ( 36H LOAD TYPES MUST NOT BE NEGATIVE) 04816 

72 FGEMAT 48B LOAD TYPE GEEATEB THAN TOTAL NUMBEB OF LOAD, 04817 
2 16H TYPES SPECIFIED) ' 04818 

73 FO EH AT (//,51H ALL EEKAINING LOAD TYPES INCBEASED BY SAKE PEBCENT, 0481 9 
* /) 04820 

DI3ENSION DITTO (21 04821 

DATA IIOVEF /IE*/, DITT /4HDITT/ 04822 

CCM2E.il - CHECK FCfi LCAD SEDUCTION 04823 

IF ( NLB .EQ. ) GO TO 102 04824 

FAC = T.O - PCBHL / 100.0 04825 

NC6 = 04826 

IF ( NLT .EQ. ) GC TO 9900 04827 

DO T010 LIT = 1.NLT 04828 

NCDLT = NCBL (LTT) 04829 

IF { NCDLT .EG, ) GO TO 1008 04830 

DO t005 II = T, NCDLT 04831 

NC6 = NC6' + 1 04832 



IF ( I0VELJNC6) .EQ. IICVEE ) GO TO 1005 04833 

FAC 
QZL{NC6) = QZL{NC6) * FAC 04836 



OJCL(NC6) = QXL (NC6) * FAC 04834 

QYL(NC6{ = QYL(NC6| * FAC Q4835 



1005 CONTINUE 04837 

GO TO 1010 04838 

1008 CONTINUE 04839 

IF { IOVBfl(LTT) . EQ. IICVES ) GO TO 1010 04840 

UQX (LIT) = UQX (LTT) * FAC 04841 

(TOY (LTT = UQY LTT) * FAC 04842 

1010 CONTINUE ' 04843 

PRINT 19, PCBftL, NLE 04844 

GO TO 9900 04845 

1020 CONTINUE 04846 

COHMENT - PRINT TABLE HEADING 04847 

PS1KI 9 04848 

IF (KEEP6 .HE, 2) GO TO 110 1 04849 

IF JNLTL .EQ. 0) GO TO 8620 04850 

PKINT 17 04851 



269 



COMMENT - 



1025 

PBII 
COMMENT - 
fiEAI 
PHI1 



NC6 = 

NCR6 = 

DO ?OH EACH OLD LOAD TYPE 

DO 1080 JJ = 1,NLTL 

IF ( JJ ,EQ, 1 ) GO TO 1025 

IF (DITTO (1). EQ.DITT ) GO TC 1027 

CONTINUE 

IF (NCE6 .EQ. NCD6) GC TO 8560 
NT 10 

HEAD LOAD TYPE AND PERCENT INCREASE 
D 21, LIT, PEE, DITTO 
NT22, LIT, PEE, DITTO 

IF ( DITTC(1) ,EQ. DITT ) PfilNT 73 
NCE6 = NCR6 ♦ 1 

IF (JJ . NE, LTT) GO TO 8650 

T T T =: JJ 

FAC = 1.0 + PEE/100,0 

NCDLT = NCDL (LTT) 
IF (NCDLT .EQ. 0) GC TO 1040 
COMMENT - INCREASE GENEEAL LOADS 
DO J030 II = 1,HCDLT 

NC6 = NC6 + 1 
IF ( I07RL(NC6) , EQ. IICVEH ) GO TO 1030 

2XL(Nd6) = QXL(NC6)*FAC 

QYL?NC6j = QYL(NC6j*FAC 

CONTI§g| hiC6j = 2 Z ^ N ")*^ 

GO TO 1080 

CONTINUE 

INCBEASE UNIFORM LOADS 

IF ( IOVRflj(LTT) .EQ. IIOVEE ) GO TO 1080 



1027 



1030 

1040 
COMMENT 



1080 



UQX LTT) = UQit(LTl)*FAC 
UQY(LTT) = UQY(LTT)*FAC 
CONTINUE 

IF (NLT . NE. NLTL) GO TO 1260 
IF (NCR6_.LT. NCD6) GO TO 8580 



0) NLTL = 
. AND. KESP6 



GO TO 9900 
1101 IF (KEEPS .EQ 

IF JNCD6 .EQ. 

GO to 1 120 
1110 PKINT 24 

P (NLT .NE. 0) GO TO 8570 



.EQ. 0) GO TO 1110 



1120 



PR 

Pfi 

1150 

COMMENT ■ 
1160 

1200 



0) GO TO 1150 
NLTL) GO TC 8570 



1240 PRI 

1250 

1260 



GO TO 9900 
IF (NCD6 .NE 
IF JNLT . NE. 
[NT 17 
:tlT 23 

GO TO 9900 
CONTINUE 

IF JKESP6 .EQ. 1) GO TO 1240 
• IKITILIZE CCNTEOL CONSTANTS 
DO 1200 I = 1,MNLT 
SC6 1 (I) = -1 
NCDL(li= - 1 
NC6 = 6 
GO TO 1250 
NT 17 



IF (NLTL -EQ. 
CONTINUE 



0) GO TO 1160 



NCK6 = 
CONTINUE 
NT 14 
DO FOR EACH LOAD TYPE 
DC 4 900 J J =1,KIT 
COHHESI - SKI? FOE LOAD TYPES HELD FRCM PREVIOUS PROBLEM 
IF (NCDL(JJ) . NE- -1) GC TO 4900 
IF (JJ .EQ. 1} GO TO 1300 
IF (JJ .EC KLTL + 1) GC TO 1300 
IF JNCDL(JJ - 1) .GT. 0) PRINT 14 
CONTINUE 

IF ]NCfi6 .EQ. NCD6) GO TO 8560 
READ AND ESINT FIRST CAED FCE LOAD TYPE 
D 12, LTT,aQXT,UQYT,NCDIT,IAXOPT,IOVEST 
NT 13, LTT,UQXT,UQYT,NCDIT,IAXOPT,IOVEET 
IF (IAXOPT .LT.1 .06. IAXOPI .ST. 4) GO TO 8590 
NCR6 = NCE6 + 1 
LTT .GT. NLT) GO TO 8720 
LTT .LT. 0) GO TO 8710 
IT) 



pri; 

COMMENT - 



1300 

COMMENT - 
REA 
PSI 



(JJ ,NE. LIT) GO TO 8650 

(NCDLT .LT. 0) GO TC 8600 
( LTT .EQ. ) GO TC 1350 



1350 
COHHENT 



COMMENT 
COMMENT 



H = MLOAD ( LTT) 

MPl = M+1 

MP2 = M + 2 
CONTINUE 

IF (NCDLT . GT. 0) GC TC 2400 
UNIFORM LCADS ONLY 
IF (IAXOPI .EQ. 1) GO TC 1500 
IF (lAXCPT .EQ. 2 GO TC 1400 
AXIS OPTICN 3 0! I) - CCNVEET UNIFORM 
AND INTENSITY OF MEMBER AXES 

TEMPI = DCIL(LTT) 

TEMPi = DC2L(L'IT) 
IF ( TEMPI .LT. 0.0) TEMPI = - TEMPI 
IF ( TSBP2 .LT. 0.0) IEMP2 = - TEMP2 

UQX(LTT) = UQXT*EC1L(LTT) *TEMP2 + 



OADS TO DIRECTIONS 



94852 

04853 

04854 

04855 

04856 

04857 

04858 

04859 

04860 

04861 

04862 

04863 

04 864 

04865 

04866 

04867 

04868 

04869 

04870 

04671 

04872 

04873 

04874 

04875 

04876 

04877 

04878 

04879 

04880 

04881 

04882 

04883 

04884 

04885 

04886 

04887 

04888 

04889 

04890 

04891 

04892 

04893 

04894 

04895 

04896 

04897 

04898 

04899 

04900 

04901 

04902 

04903 

04904 

04905 

04906 

04907 

04908 

04909 

04910 

04911 

04912 

04913 

04914 

04915 

04916 

04917 

04918 

04919 

04920 

04921 

04922 

04923 

04924 

04925 

04926 

04927 

04928 

04929 

04930 

04931 

04932 

04933 

04934 

04935 

04936 

04937 

04938 

04939 

04940 

04941 

04942 

04943 

04944 

04945 

04946 

04947 



270 



uyy(LXT) = -08 



CGBBENT 

COHBENT 

1400 



COHBENT 
1500 



GO TO 1600 
AXIS OPTICS 

MEM BEE AXIS 

JJQX(LIT) 

GO _ 
AXIS 



UQYT*DC2_ 

UQXT*EC2L|lT-I 

UQYT*DC1L(LTT 



'I (LIT] 



*TEMP1 
*TEHP2 
*TEHP1 



2 - CONVERT UNIFOEH LOADS TO DIRECTIONS OF 



UQY jLTT) 
TO 1600 



UQXT*DC1L(LTT) + 
- UQXT*DC2L(LTT) 



DQYT*DC2L{LTT) 
+ UQYT*DC"}L(LTT) 



1600 



COBMENT 
2400 



COMHENT 



SSx(lIT) 1 = OQXT S AILEEAEI IN HEHBEfi AXES 

DQY(LTTJ = UQYT 

NCDL(LTT) = 

IAXGPL(LTT) = IAXOPT 

IOVRH(LTT) ' = IOVEE1 
GO TO 4900 
VARIABLE LOADIHG 
CONTINUE 
IF (UQXT ,NE. . 

SCDL(LTT) = 

IAXOPL(LTT) 
PRINT 18, LIT 



.OR. UQYT 
NCDLT 
IAXOPT 



.NE. 0) GO TO 8670 



DO 

DO 



COMKENT 

READ 
PRINT 



if 
IP , 

REAL 



jfSS- EACH ADDITIONAL CARD OF LOAD TYPE 
4500 II = 1.NCDLT 

NC6 = 8C6 + 1 

• EC. 1) NCS1U.TT) 

--6.EQ, NCD6) GO TC 

AND PRINT 



i 11 
(NCR! 



COHBENT 
2600 



2700 

2800 
COHHEN1 - 



Tfl 

CONVERT 

GO TO 

XL 
XE_, 

GO TO 2800 



CD6) 

HONUNIFOBH 



= NC6 
8560 
LOAD 



DATA 



Ifi' Uf\lM\'^V^M"'UH^Ul'''^ L i VC6 \ ,ICVBL{NC6) 
HCR6 = »6fi6 ♦ 1 ' »QXLT,QYLT,Q2L|HC6),IOVEL(JiC6) 



= ZLL(LTT)/fl 
DISTANCES TO HEHBER 



COORDINATES 
IAXOPT 



CONTINUE 
CHECK FOR 



(2800.2800,2700,2600), IAXC 
LIJNC6S = XLLfNC6)/DC2L(LTT) 
^i? c6 J = XEL(NC6)/DC2L LTT) 

2800 

XLL(NC61 = XLL(NC6)/DC1L(LTT) 
XHL(SC6) = XEL(NC&i/'DC1L(LTTJ 



IF 

IF 
IF 
IF 
IF 
IF 



iXLL 
XRL 
XHL 
II .EC. 
XRL (NCb 
XLLJNC6) 



NC6 
NC6 
NC6 



ILLEGAL DATA 

.LI. 0.0) GO 

.GT. ZLL(LIT) 

•EQ. 0.0) GO 

1) GO TC 2820 

1) .NE. 0.0) 

NE. 0.0) GO 



TC 

+ 

TO 



8540 
0. 1*TH) 
2838 



GO TO 8520 



GO TO 2820 
TO 85 50 



2820 
2830 
2838 



2840 



CO BS EN T - 
CC8BENT - 



GO 

IF 

IF 
GO 



DSL = XRL(NC6) - XLL (NC6 - 1) 
TO 2830 

DEL = XRL(!IC6) - XLL(NC6) 
(DEL .EQ, 0.0) GO TO 2840 
(DEL .IS. TH) GO TO 8530 
TO 2840 

DEL =1.0 
IF (II .EQ. 1) GO TO 2840 
IF JXLL(NCfa) .EQ 
CONTINUE 

IF (IAXOPT .EQ. 1) GO 
IF (IAXOPT .EQ. 2 .OR 
AXIS ACTIONS 3 Cfi 4 - 
AND INTENSITY CF HEBBEE AXES 
TEBP1 = DC1L (LTT) 
TEBP2 = DC2L (LTT) 
TEBP1 .LT. 0.0) TEHP1 



.AND. XRL(NC6 - 1) . EQ. 0.0) GO TO 8610 



TC 2900 

. DEL .EQ 
CCSVEBT 



. 0.0) GO . 
DISTRIBUTED 



TO 2850 
LOADS 



IF 
IF 



2850 
COMHENT 
CCfiBENT 



2900 
COHMENT 



T2BP2 .LT. 
QXL(KC6) = 

QYL(SC6) = 

GO TO 2950 

CONTINUE 

AXIS OPTION 2 Ofi 

AND CONCENTRATED 
QXL (NC6) 
QYLJNC6) 

GO TO 2950 

CONTINUE 

AXIS OPTION 1 - 



0.0) IEHP2 
QXLT*EC1L| 
QYLT*DC2Li 

-QXLT*CC2Li 
QYiT*DC1Li 



TEBP1 

TEBP2 

*TEBP2 

*TEHP1 

*TEMP2 

*TEMP1 



CONCENTRATED LOADS - CONVERT DISTRIBUTED 
LOADS TO DIRECTIONS OF HEBBEE AXES 
QXLI*DC1L(LTT) + QYLT*DC2L (LTT) 
-QXLT*DC2L(LTT) + QYLT*DC1£ (LTT) 



QXL(NC6) 
QYL(NC6) 



2950 CONTINUE 
45U0 CONTINUE 
4900 CONTINUE 

IF (NCS6 . 

GO TO 9900 
«520 PHINT 52 

GO TO 9700 
3530 PRINT 53 

GO TO 9700 
o540 PRINT 54 

GO TO 9 70C 
8550 PRINT 55 

GO TO 9700 
8560 PRINT 56 

GO 10 9700 
3570 PHINT 57 



LOADS 

QXLT 

QYLT 



ALLREADY IN MEBBER AXES 



LT. NCD6) GO TO 8580 



mi 

04950 
04951 
04952 
04953 
04954 
04955 
04956 
04957 
04958 
04959 
04960 
04961 
04962 
04963 
04964 
04965 
04966 
04967 
04968 
04969 
04970 
04971 
04972 
04973 
04974 
04975 
04 976 
04977 
04978 
04979 
04980 
04931 
04982 
04983 
04984 
04985 
04986 
04987 
04988 
04989 
C4990 
04991 
04992 
04993 
04994 
04995 
04996 
04997 
04998 
04999 
05000 
05001 
05002 
05003 
05004 
05005 
05006 
TO DIRECTIONS 05007 
05008 
05009 
05010 
05011 
05012 
05013 
05014 
05015 
05016 
05017 
05018 
05019 
05020 
05021 
05022 
05023 
05024 
05025 
05026 
05027 
05028 
05029 
05030 
05031 
05032 
05033 
05034 
05035 
05036 
05037 
05038 
05039 
05040 
05041 
05042 
05043 



271 



.«-, GO TO 9700 

OidJ PRINT 58 

-.„„ GO TO 9700 

8590 P11H1 59 

... GO TO 9700 

8600 PRINT 60 

..,„ GO TO 9700 

d610 PRINT 61 

GO 10 9 700 
6620 PB.INT 62 

GO TO 9700 
8os0 PRINT 65 
„„_ GO TO 9700 
8670 PRINT 67 
„,„, GO TO 9700 
8710 PHINT 71 

„„ GO TO 9700 
8720 PEINT 72 
5700 IAEAN = 1 

9900 CONTINUE 

NLTL = NLT 
RETUBN 
END 



mn 

05046 
05047 
05048 
05049 
05050 
05051 
05052 
05053 
05054 
05055 
05056 
05057 
05058 
05059 
05060 
05061 
05062 
05063 
05064 
05065 
05066 



*****5u1eS0TINE*ITC0NT************ SaBHOUTIHE ******************************* 

%Um - SSS'gSli'fiFSgS ttfgii Sfi" 10 " C0RTH0L DATA - CHECKS P0E 



IMPLICIT REAL*8 (A-H,0-Z) 
fY{25f, 



CCM20N /BLOCK1/ x'(25 

2 QZZ(25), SXX 

3 DYY(25i, D22 

4 ERXX(25f, ERY 

5 NSXX(25 ; NSYY(25,, 

6 NSYPJ25), ISTJg<25) 
COHHOH /jjiOCfttt/ goaaii0,6) ,SMC(50,211,IST(50) 



SYY(25) , 
RXXJ25L , 
ERZ2(25) , 
NSZZ(25) , 



C2X(25) 
SZZ/25) 
RYY 25} 
QSJ 25 
IHJ 25) 



QYY{25) , 
DXX (25), 
EZZ(25j: 
WMJ 2 5J . 
HSX?(25) , 



2 JT1'I50J \ ." ' JT2"(50)";""'"""NiTfil5bf"" JJL i^'^Ol 

COMMON tBd^ T0L 6 ; b |iEHNT,N||iJ! 5 lkp3i^i3°|:,: 

KEEP5 



(50) 
IMC (50) 

3 
4 
5 
6 
7 BP1, " HP2""' ISTT, LTtI ITY&EL tdi' nStt 

^ r ,„„ , „ BNlIM.NSflJ.NSHB 
CCKHOH / BH / PCSBL, PCRJL, NIB. SLBA 
COMMON /SKT21/ NTH, NTBA 
COMMON /GT/ MJO 

1ABLE_7_- ITERATION CONTROL 



, KEEP3A,KEEP3B, K£EP4A,KEEP4B, KEEP4C.KEEP5 A 
£,KEEP5C,KEEE5D'KEEP6, KE2P7, NCD2. NCD3A 
HCD3B, NCD4A, NCD43, NCD4C, NCD5A? NCE5B NCD5C 
NCD5D, NCD6, NCD7, IP8, IP9. IP10 ITYpS' 
IABAN, IfQai. NM, NJT,' iff* g{J* I""' 



** 
05067 
05068 
05069 
05070 
05071 
05072 
05073 
05074 
05075 
05076 
05077 
05078 
05079*79 
05080*61 
05081*61 
05082*61 
05083*61 
05084*61 
05085*61 
05086*88 




///) 



% 



4 3SHRED.PRCNI JOINTS 
1i( .i F SSSiLi^/*3 5 ?X?8gP*3fI«fi. AND MEMBER SO 



FORMAT 
FORMAT 
FORMAT 
FORMAT 

74 FOBMAT 

2 30HEIT 

3 8HNEGA 

75 FOSKAT 
2 30IiEITfiE 



05087*88 
05088 
05089 
05090 
05091 
05092*88 
5 9 ^ ♦flfl 
EVIOUS PBOBLEB,///) 05094 
TIME NUMB NUMB FORCE, 5X05095*88 
__„_ „„„ BONITOB, /,05096*88 
TIBE STEP , 05097*88 
$ G l$ TS *.//\ 05098*88 

LOTIONS.// ,3X,4HDAMP,5X, 05099*88 

. 05100*88 

ITER, 05101*88 

M3ERS, 05102*88 

05103*88 

"' *88 

88 




3 8HNEGATIVE) 

2 F °5HOhDEaf H h0liltaB flEHB£ 6 KUM3EES HAVE TO BE IN THE 1SCENDINC 
77 FOBMAT (4 

1511 MONITOR JOINTS) 



JoV JOINTS?* HCNITCK j OI»TS IS NOT EQUAL TO INPUT, 
7 Vl6TyfTOR N flL?I!Bsf MCNITCR HEHBEBS IS N0T E 2 UiL T0 ""I, 



COM 



"A°^hk Ta1l H E HEADInI"" 7 " HELD NC CAEDS » AY BE 40D2 °) 
PRINT 9 



IF (KEEP7 .EQ 
IF (KEEP7 .EQ. 
READ 14, NLEA.NTRA 



1 .AND. NCD7 
1) GO TO 2010 



.NE. 0) GO TO 8700 



READ 15. 
GO TC 
2010 PRINT 17 
2100 PRINT 18 
PRINT 24, 
2 ' 
IF ( 



(MJ(lf,I=1 20? E ' NTI ' EaB1 ' £BE2 ' DTI ' i ' C8JL ' NSHJ ' 
C 2100°' MNI * H ' ' EE2,PCEML ' NSHM ' f""^) »I=1»20 

J.i>J I X J ,1- I ,2U) 
NSMJ.GT.20 ,OB. NSMJ.GT.NJT .OR. NS M 



PCRJL,NSMJ, 
MJ.LT.O) GO TO 8740 



05109*88 


05110*88 


05111*88 


05112*88 


05113*88 


05114*88 


05115*88 


05116*88 


05117*89 


05118*89 


05119*89 


05120*89 


05121 


05122 


05123 


05124 


05125 


05126*88 


05127*88 


05128*88 


05129 


05130 


05131 


05132*88 


05133*88 


05134*88 



272 



11 iWl = G V 2 ^ 0) G ° T ° 871 ° 05135 

2200 CONTINUE* - GX: NJI -° B - " J(I) ' LT ' °> G0 T0 8720 05137* 88 

PRINT 26 MJO 05138 

26 PRINtS^' 3 ° H M01iIT0E J0ISI OUTPUT OPTION =,15,/) 05140 

PHINT 25, C3,i5JC,KNrr»,IE1,ER2,PC2BL, NSBH, (SS(I) ,1=1.20) 0S14?*fiA 

g jjg!|"4j 8f ' B'folriB N ^ H -^ 5 > g6 ° c 875 ° HljjJH 

IF (KSEP7 .EQ. 1) GC TO 9900 oVAl 

12 JNSBfl .LI. 2) GO TC 3510 olluf»fl«J 

D0 iiV-V: i H oiisCT 

3500 £Si^s } - LT - WH(ifl1)) gc to 876 ° Silsgl! 

3510 CONTINUE 95153*88 

S2SSISI " SET J °iNT SWITCH EQUAL TO 1 FOB BONITOR JOISTS nsiiS 
COHBENI - CHBCK^SHJjTHEH SPECIFIED NDMBEB OF HCNITOBJOINTS ARE INPUT 05156*89 

DO 3600 I = 1.HJT nll^R* 89 

DO 3600 V = 1,20 oflfiO*flB 

" (I i«wt»"W }) G ° T ° 36 °° 05161*89 

J600 CONTINUE nticn 89 

r. ■<***, -n. IF (KOUNT . NE . NS HJ) GO TO 8770 051fi£*flq 

SiiSSiSS - SET MEMBEE SWITCH EQUAL TO 1 FOB HCNITOB BEaBEPS n^lfifi 
COBBENI - CHECK WHETHER SPECIFIED KOHBEB CP HCSITOfi BEhIIIs ftEE INPUT 05167*89 

DO 3800 UN ! = ?,NB gllli* 89 

IH8 (I) = 6 oii7n 

DO 3800 J '= 1 20 oil7i*aa 

IF (I .Eg. HiS (Jjl IBHjfll = 1 05172 

IF '^^"W" GO TO 3800 05173*89 

ioWi'- kodht ♦ 1 8iws:s8 



3800 CONTINUE nti-rc 8 

GO }o°9900' SE ' NSMfl) GC T ° 878 ° 05177*89 

87UO PEINI 87 " nf J3§ 

GC TO 9700 85 I' 

8710 PRINT 71 acIq? 

GO TO 9700 SgJSJ 

U720 PRINT 72 nllli 

a _„ r GC TO 9700 Q§1§3 

373J PHINT 73 °J. 1 §^ 

GC TO 9700 OblBo 

8740 PEINT 74 05186*88 

GO TO 9700 05187*88 

8750 PEINI 75 WJIIIII 

GO TO 9700 05189*88 

d760 PRINT 76 05190*88 

GO TO 9700 05191*88 

°770 PEINT 77 SL 19 , 2 ! 8 ?, 

GO TO 9700 05193*89 

87b0 pa 1ST 78 05194*89 

9700 IABAN = 1 Sill!* 89 

9900 CONTINUE °5196 

fiEIUBN 05197 

END 05198 

05199 



"mSIm - SKHt(l" H ? ADVANTAGE OF SYHETBI SICeL IN CCHPACT VBCIOB * 05202 

COHaENT = SHOWN BFLCH 6 S * IFfNESS « ATfiI * ST0 *SD AS 2 1 I 1 VECTOR SMUT AS 05204 

COMMENT - 1 ' s K r 2IS2I 

CCHHEST - 2 7 Y I L 05206 

COBBENI - 3 8 12 9 r 8I1S2 

CCfifiEHT - 4 9 13 16 B A nlonn 

COHHEN-I - 5 10 14 17 19 g SIl?2 

COHHENT - 6 11 15 ifi in oi * 05210 




05211 
05212 

f"li! L1,f Iilii;, nii.^- W'Jfi- nw- 

I 5??9*L? 5 )' J"JM 25J, IPINB( 25), NC51( 25). INLOPf 25) 0521 P*U? 

ri/l^Mflh ffifcj. 11,1;. 11,1; Hi 



273 



05228**5 



CQ3A0K Vjiogfj/ S|jS| 1| ill&JtW. lilaKlo). 01120,10), 81111 

2 C0 a3 0K B /BL0C V KPT, {20), 131,(20), MQH {20.11). 118(20.11). Ml 

COMMON /BLK1/ TCL, ELEMNT, NJST. KEEP3C. NCD3C nlllLlQ 

g|||: est;- is*;- !ir- S8?» : Iff ■ 111 I ;! 

2 pipfes pi & t at%ju-bniH<iist:iBi^iein.. |, 

COMMON /BLKU/ ST1.ST2 ST3 ^TU qTR cw 05244*79 

COMMON /5KT5/ ' ftSXH (21,10), WKIM (21,10), WRZH (21 101 05250 

COEflON /SKTU^ EPH1S(21,10,3],eIIt1S(21,10,3), gff f^ 

05259 
SLBF1 (21,10,3), 05260 
£FEFT2l21,10;3 K 05261 

05262 
EPSPRE (21,2,10) , 05263 




3 SLBF2 

3 E? 

5 yg 



SLBF2 21 10 j K SLBFT2 2 ' O,'! 
KPSKAX 21,2.b K EPSHIS'21,'2,15 

"coaaoH /SKI35/ SUV' 1 ' 2 '™'' "Mostfi.f.tfj- - «||| 

Tp , be* iov>iyis<a/ l,o " E /5hanon2/ -I 

IF ( ITYPE LE 2 1 TMP9TP - ihphp U52o/*16 

COHaEST - SET IMBOMHT CWllfll CONSTANTS FOB STIFF TYPE ISTT §5269 

dpi- B+1 (ISTI) 05270 

MP2= B+2 05271 

IPINLT = IPINL(ISTT) 3|§2i 

IPINET = IFINH(ISTI) nltnt 

ZL = ZLS(ISTT) ' Q522» 

NCDSI = NCDS(ISTl) 5^L 5 

SC51I = NC5l]lSTT[ 95276 

INLOPT = INLdP(ISTT) nkVtl 

MODELT = HCDEL ISTT SISZ| 

ELEMNT = ELEMN(ISIl[ ftfonn*in 

IF ( INLCET .EC { GO TO 1000 nt?Bi 10 

KALI = NAL(ISTT) ncoqo 

NCDAT = NCDA (ISTT) 03282 

1000 CONTINUE" = KS2 MiSTT) + NSYl (ISTT) + »SZL (ISTT) 8tl" 

CCBBE£1 - COMPUTE CONSTANTS FCH MEMBEE SOLUTIONS FOE STIFFNESS VALUES 05286 

B * 0. 5*TH 05287 

HSQ = H*H 05288 

HCU = HSC*H nllot 

NL = 3+MP1 05290 

ML = 1 U3291 

NFSUE = 22 05292 

liggM -Eg. SHEAB ) GO TO 5000 05?9U**ft 

THESTP .EQ. ANEH ) GO TO 1200 0529S 

ITYPE .GS, 3 ) GO TO 1300 0S7QK 

KITF .at, 1) G& TO 1200 ' n\lli 

4 * ilTYPE .EQ. 2) GC TO 1200 nco2a 

COMMENT - ZEKO^EMBE^DISpIaCEMENTS §|jl| 

gfia : o° : o° 8B8? 

1150 gljll = g'.G 05302 

i r F I ffil T :i: 3 J g§ ? ° ]?§8 §||8| 
SSSfiH : foTf i | I fI | E| a coffI s «R ,1%",%^ agp |} B ^B NnR IP 

DO 1155 J = 1*1fl 05308 

KHXM (1,5) = 0.0 ll\^l 

BBTXfi(I,Jj = 0,0 niiii 

WEYH (I, J) = 0.0 n^io 

*aTYM(I,Jj = 0.0 nilii 

BEZH I, J = 0.0 cM\l 

,, r - KETZM(I,J) = 0.0 8113c 

1155 COIITINUE V ' 0531 5 

SS3S1S2 - 585?i»iiSI EEVEESAL CHECK ISDICATOFS F02 ALL TRV thufb n^, 1 ? 



BBSU - INITIALISE EE7EESAL CHECK ISDICATOFS FO" ALI TB' tbopf S^ S 

MNT - 8BHBB|-S0M0M SPHIHci AT CMB1 OFEACH ELEMENT TH5EE SlllS 

DO 1157 N = 1,'3 F1 05319 

aCU&ET(I,lf) = 05321 



274 



1 J 57 CONTINUE 

1158 CONTINUE 

. IF I MODELT .LE. -1 
S8S5122 " INITIALISE EPSILONE 
COMMENT - AT BOTH HINGES ( 1 
COMMENT - AND MSSIM1 COrfPO 



1160 

COMMENT 
COMMENT 



COUPON 

2,mpi 

1, MNPCS 

1,MSSIH 

I,J,K' 

I,J,K 

I,J,K 



j.j.k' 



1165 

COMMENT 
COM flt NT 

COMMENT 
COMMENT 



= 
1.NCDAT 
= NSS(N 
= NDIV 

= NSIG 
= NEPS 



1170 
1175 



1177 

1180 
1185 

COM .IE 
COMME 



1195 

COi.i£ 
1200 



COMriE 
COMME 



COS8E 

1250 

COMME 



- AND MSSIM1 
DO 1160 I = 
DO 1 160 J = 
DO 1160 K a 

EPfi IS 

EPET1S 

EPR2S , 

EPET2S {l,J,K 
CONTINUE 

IF ( MODELT .EC 
' INITIALISE BIFUECAT 
1 VALUES ALSO FOE HI 
DO 1165 I = 2,MP1 
DO 1165 J = 1,SEPCS 
DO 1165 K - 1,BSSIK 

EPBF1 

EPBFT1 

SLBF1 

SLBFT1 (I,j;k 

EPBF2 (I#J»K 

EPBFI2 (I,J,K 

SLBF2 (I,J,K 

SLBF12(I,J,K 
CONTINUE 

ASSIGN PROPER INITI 
PREVIOUS STfiAIN, YI 
FOE EACH SUBEECTANG 
OF EACH EL2BENT. 
DO 1180 I = 2,BP1 
DO 1180 L = V,2 

ICUMU 
DO 1175 J = 

NSSLI 

NDIVT 

SIGMA 

PSLCN 
DO 1 170 IDVT = 1,ND" 

icuau = icOmu 

EP5fiAX(I,L,ICU 
EP5HIN (1,1, ICU 
EPSPEE(I.L,ICU 
IF ( HGDELT . KE. 2 
YGROW (I,L,ICU 

XTSEOS 

CONTINUE 
CONTINUE 
IF { ICUMU ,G 
IBEGIN = 
DO 1177 ICUMU 
2PSBAX (I 
EPSfilN I 
EPSPRE(I 
IF ( MODELT . 
YGROW (I 
YTGRC* 
CONTINUE 
CONTINUE 
CONTINUE 
*2 - INITIALISE 
NT - HINGES 1S2 
DC 1195 I = 
DO 1195 L = 
DO 1 195 J = 

IKV ( 
CONTINUE 
GO TO 1300 
NT - BEAD MEMBER 
READ (Nl) (DX[ 
IF ( INLCPT 
IF ( NEEAD 
-NT - READ 5ESIDU 
NT - SEH3EB SUPP 

READ (N1) ( { 
2»BZM(I,J),- BfilZ 
NT - HEAD REV EPS 



GO TO 1300 

EPSILCNET FOR EACH ELEMENT I , 
6 2 ), FOR A MAXIMUM OF MNPCS PIECES 
ENT 5IGKA-EPSILON CURVES 

1 

= 0,0 
= 0.0 
= 0.0 

= 0.0 

) GC TO 1185 

ION STRAIN 5 SLCFE AND THEIE TEMPORARY 

b£3 1 o Z • 



1 

= 0.0 
= 0.0 
= 0-0 
= 0.0 
= 0.0 
= 0.0 
= 0.0 
= 0.0 

AL VALUES TO MAX. STRAIN, MIN. STRAIN, 
?i D S!°K!! LEVEL, S ITS TEHPOEABY VALUE 
LE OF THE CBOSS SECTION AT BOTH HINGES 



ALT, 
NALT 
NSSL 
NSSL 
IVT 
+ 
SU 
HO 

BO, 
j GC 
BU) 



% 



f,2) * SB(NALT,J) 
1,2] * Ei!(NALT,JJ 



1 

= PSLON 
■ -PSLCN 
= 0,0 

TO 1170 
= SIGMA 



(I.L.ICUHU) = SIGMA 



£, M 
ICO 
= I 
,L,I 
#L,I 
,L,I 
NE. 
,1,1 
#1.1 



NPCS ) 

MU + 1 

BEGIN 

CUMU 

CUHU 

CUMU 

2 ) 

CUMU 

CUMU 



GO TO 1180 



MNPCS 

PSLON 
-PSLON 
0.0 
TO 1177 
= SIGMA 
= SIGMA 



REVERSAL CHECK INDICATOR FOR EACH ELEMENT, AT BOTH 
, FOR A MAXIMUM OF MNPCS SOBRECIANGLES 
2 , MP 1 

I ' 2 

1 , MEPCS 

1,1, J ) = 



DISPLACEMENTS 



dz(i) , i 

GO TO 1300 



1,3P2) 



-Eg. ) GO TO 1250 
AL S TEMPORARY RESIDUAL DISPLACEMENTS OF 
OfiT CURVES f THEIR COMPONENTS ) 



6(I(|1), J=1,1Q), I=2,MP1 ) 
..-AL INDICATORS FOR MEMBER-SUPPORT SPRINGS 
COtiTINui' °* EV(I ' N) ' N=1 ' 3 >' I = 2#HP1 ) 



N'l 

REA 
2 



REA 



IF ( MODELT 

READ RESIDU 

JO (Nl) ((( E 

EP 
IF ( MODELT 
D (N1 ) 



READ (Nl ) 

2 

IF ( MODELT 
READ (Hi ) 



LE. 
AL C T 
5(1 
RT2S (I 
. EC. 
(((EPS 
SL3 
SLB 
J = 
(( (EPS 
J ■ 
. NE. 
(((YGH 
L = 



-1 ) GO TO 1300 

EMPORARY RESIDUAL STRAINS 

,J,K) , EPfiT1S(I, J,K> , EPR2S(I,J,K) , 

'o'f'GC TO = 126G SSIfl1 '' J=1 ' HHpts f' f=2,MP1 ) 



F1 '(I,J,K) , EPBFT1 (I,J,K 
I,J,K , EPBF2 (I,J,K 



slbfi2(i:j;k 

I = 2.HP1 f 



SLBF1 (I,J,K), 
EP3FT2Jl,J,K) , 
K=1,HSSIH1 ), 



FT1 

F2 Jli-J, Ki 

2 ) GO TO 1260 ' ' 

OW (I L.J) , YTGRCW (I,L,J) , J = 1, MNPCS ), 
i,2), 1 = 2, MP 1) 



ffitt 

05324 

05325 

05326 

05327 

05328 

05329 

05330 

05331 

05332 

05333 

05334 

05335 

05336 

05337 

05338 

05339 

053UO 

05341 

05342 

05343 

05344 

05345 

05346 

05347 

05348 

05349 

05350 

05351 

05352 

05353 

05354 

05355 

05356 

05357 

05358 

05359 

05360 

05361 

05362 

05363 

05364 

05365 

05366 

05367 

05368 

05369 

05370 
05371 
05372 
05373 
05374 
05375 
05376 
05377 
05378 
05379 
05380 
05381 
05382 
05383 
05384 
05385 
05386 
05387 
05388 
05389 
05390 
05391 
05392 
05393 
05394 
05395 

05396 
05397 
05398 
05399 

05400 

05401 

05402 

05403 

05404 

05405 

05406 

05407 

05408 

05409 

05410 

05411 

05412 

05413 

05414 

05415 

05416 

05417 



275 



1260 CONTINUE 
COasm - BEAD BKVEBSAL INDICATOBS FOB STEAINS 

~ ill (((IB7(I,L,J),J=1,HNPCS) ,L=1,2),I=2,HP1) 



1300 
COMMENT 



1300 



:ONTINtji 



- ZEBO MEMBER INCREMENTAL LOADS 



DO 1800 1 

EEX (I 

EHZ (I 

ERZ]l 

IF (INLGPT 

IF (NCDST 



= 1.MP2 
= 0.0 
= 0.0 
= 0,0 
EQ. 1) 



, GO TC 2400 

COaifsT - R B A V irIr"ip C lz DISCHETIZES MEMBER LINEAB STIFFNESS DATA 

" CALL GO To'2500 CST ' ( NC51T ' NCDST ' ZL ' L1 ) 
2100 CONTINUE 

COMMENT - PEIS&ATIC BEMBEfl WITH CONSTANT F AND AE 
PiiFT = PHF(ISH) 
PEAET = PBAEflSTT) 

i,hp2 

0.0 
0.0 
0.0 
0.0 
0.0 
0.0 
AEfl) = PfiAET 
PBFT 



DO 2200 
SX 

ST 

sz 

SQ 

SQY 

SQZ 



I = 

u 



2200 



2400 



2405 



Fit) 

NUE 



V 



COHTIN 
AE 
AE 
F(1) 

GO TO 2500 
CONTINUE 
IF ( TMES1P 



(1) = 
JHE2) 



..0 
= 0.0 
0.0 
= 0.0 



IF 
CO 
IF 
DO 



( THE 
l ITY 

NTINUE 
BE 

_ 
X (I 

Y II 

1 , T 



PE -GE 



EQ 



. ANEM ) GC TC 240 5 
3 ) GO TO 2600 



7. N3EAD 



I = 



2410 
2420 

comment 

COMMENT 
COMMENT 

CALL 

5000 



comment 



.NE. 
1,HP2 
= 0.0 
= 0.0 
= 0,0 
= 0.0 
= 0.0 
= 0.0 



) 



5150 



COMflEUT 
COMMENT 



5155 
COMMENT 
COMMENT 



5157 

5156 



IF ( 

OMMENT - INITI 



4l5 -= .- GO TO 2420 

SX 
SY 
SZ (L, 

SQX i I) 
SQY ill 

SQZ (I) 
CONTINUE 
GO TO 2500 
CONTINUE 

SUBROUTINE NLSS DISCHETIZES DISTRIBUTED HEIBFR O - B mvwz 
Ko'liSxiS JlI?M E §I «If ^IVE S H pIl BD Nl E F D og C ^S BEH S Q QX. SQY^sfz 

.0 TO 2loi S ( L1 ' " > ' ' 

CONTINUE 

IF (IMESIP .SQ. ANEW) GO TO 5200 

IF (ITYPE . G3. 3) GC TO 5300 

IF (NITF . GT. 1) GO TO 5200 

IF (HYPE . EQ. 2) GO TC 5200 

ZEHO MEMBER DISPLACEMENTS 

DO 5150 I = 1.MP2 

DXfl) = 0.0 

BY (I) =0.0 

DZ(l[ = 0.0 
IF ( INLCPT .EQ. ) 
AD . EQ. 
__SE OE AND 
FOP. THE THREE CUBV2S 
DC 5155 I = 2,KP1 
DO 5155 J = 1* 10 

WBXM (I, J) 

*BTXK(I,J< 

WBYM j'l.J 

SHTYK|I,J 

HBZM II, J 

«EIZH(I, J 
CONTINUE 

i"JTIALISE BEVEHSAL CHECK INDICATORS FOE ALL THE TEBEE 
HEMBEg-SUFPOST SPRINGS AT CENTRE CF EACH ELEMENT 

DO 5157 N = 1,3 

MCUBEV (I, HI = 
CONTINUE 
CONTINUE 

MODELT . LE. -1 



IF ( ISL 

IF ] NBE 
- INITIALI 



GO TO 5300 
GO TO 5158 

UET VALUES FOE EACH ELEMENT, AND 
X, Y, AND Z AND FOE EACH SUB-COMPONENT 



0.0 
0.0 
0.0 
0.0 
0.0 
0.0 



COMMENT 
COMMENT 



o16u 



ALISE EPSILONS 



AT THE HINGE, FOE A 
COMPONENT 3IGKA-EPSILQN CURVES 
Du 5160 I = 2.MP1 
DO 5160 J = J'hUPCS 
DO 3160 K = 1,HSSIM1 
EPB1S (I,J,K) = 

EPBI1S I,J,K = 

CONTINUE 

IF (MODELT .EQ. ) 
VII 



GC TO 5300 

EESILCNET FOB EACH SHEAS 



ELEHENT 



SAXxana of mnpcs pieces and mssimi 



0.0 
0.0 



COMMENT - INITIALISE BIFURCATION 



GO TO 
TBJ 



5185 
IK 6 



SLOPE AND THEIR TEMPOEAEY 



05418 

05419 

05420 

05421 

05422 

05423 

05424 

05425 

05426 

05427 

05428 

05429 

05430 

05431 

05432 

05433 

05434 

05435 

05436 

05437 

05438 

05439 

05440 

05441 

05442 

05443 

05444 

05445 

05446 

05447 

05448 

05449 

05450 

05451 

05452 

05453 

05454 

05455 

05456 

05457 

05458 

05459 

05460 

05461 

05462 

05463 

05464 

05465 

05466 

05467 

05468 

05469 

05470 

05471*18 

05472**8 

05473*30 

05474*30 

05475*26 

05476*26 

05477*26 

05478*26 

05479*26 

05480*26 

05481*26 

05482*78 

05483*78 

05484*78 

05485*78 

05486*78 

05487*78 

05488*78 

05489*78 

05490*78 

05491*78 

05492*78 

05493*78 

05494*78 

05495*78 

05496*78 

05497*78 

05498*78 

05499*78 

05500*78 

05501*78 

05502*78 

05503*78 

05504*78 

05505*78 

05506*78 

05507*78 

05508*78 

05509*78 

05510*78 

0551 1*78 

05512*78 

05513*78 



276 

COMMENT - VALUES AT THE HINGE fl«5«?m*7fl 

DO 5T65 I = 2,HP1 R5^3*-7o 

DO 5165 J = 1,MiiPCS n^lit*™ 

DO 5165 K = I^BSSIHI 0§51fi*7S 

EPBF1 (I,J,K) = 0.0 n^l«*7ft 

epbfti |i,j'k) =0.0 sStJaJ?! 

SLBF1 {I'jjK = 0.0 »«4sJ« 

5165 CONTINUE °>tlioi3§ 

jjggggi : giiSSuP&lixifii&S&gii iSfg£Nlft'i.2i8iii;% 1 , 1 I!: I 
gtiHti : KWbSBSS** 18 ** 0F THE aSs'slciigi^fPSSSHxJSl" B|ip*|| 

DO 5175 J 2 1.NCDAT llllllll 

NSSLT = NSSjNALT.J) otilnjli 

NDI7T = SDlf f NAlf Jj\ 05531*7R 

SIGMA = NSIG NSSLT, 2) * SM(NALT,J) 05532*78 

do ^mh^Amv-™ * "I-alt:j| I] : 

icomu = icfiau ♦ 1 nttf**™ 

i F ( g§i!l l ?sJl: 1 §Tfco-To 5?7o ■ iiiilxll 

YGBOW <I,1,ICUHU) = SIGHA 055UO*78 

5170 co^r * 11 ' 1 ' 1 ^ = sigsa jioga 

=175 COHTISUE fiisSiJ?! 

IF ( ps&'S'icggn \ so to 518 ° Sj3ii:3 

D0 51 g a ISK.i JSK5P = fl iI£o s K 

CPHHSgT " INITIALISE REVERSAL CHECK INDICATOR FOR FACE ELEBENT, AT THE 05556*78 

C.OHUHT - HINSE . |CS A MAXIMUM OF MNPCS SO EHECTA NGLES i,EnijMi ' A1 iH " 05557*78 

DO ?]?? I - 2 , MP1 n^ctiia 



DO 5195 J = 1 , MNPCS 



05558*78 



IBV I! 1'j \ - 1 05559*78 

5195 CONTINUE ( * ' 1 ' J ' " ° 05561*78 

GO TO 5300 0556?*;>7 

COMMENT - READ H2HBER DISPLACEHENIS 05563*26 

5200 fiEAD (S1) (DX (I) ,DY ( I) ,DZ (I), 1= 1 , MP2) 05564*26 

IF INCOPT .EQ.'o ) GO TO 530& ' 05565*78 



IF { INLOFT ,SQ, o ) GO TO 5300 05565*78 

IF ] NBEAE .EQ. ) GO TO 5250 05566*78 

COMMENT - BEAD HESIDOAL 5 TEMPORARY BESIDOAL DISPLACEMENTS OF 05567*78 

"OUHBNt - HEHBES SUPPORT CORVES ( THEIR COHEOHE" 

READ (K1) ( ( WBXM(I,J), HRTXM(I,J), BfiJ 

2WKZM(I,J) t BBIZa(I-J), J=1,10), 1=2, MP1 ) 

33HBHT - READ HEVEBSAL INDICATORS FOR MEMBER'S.. 

„ M aEa = (£3) f(MCOEEV(I,N), 1-1,3), 1=2, MP1 ) 05572*78 

5230 CONTINUE 05573*78 

IF ( HODELT .12. -1 ) GC TO 5300 05574*78 

COMMENT - READ RESIDUAL S TEMPORARY RESIDOAL STRAINS 05575*78 

BEAD (HI) ((( EPS1S(I,J,K) , EPBT IS (I , J,K) , 05576*78 



8(1, J), BP.TIM(I,J), 05569*78 

05570*78 



((( EPR1S(I,J,K) , £PBT1S(I,J,K), 
2 S = 1,MS5IM1), J=1,HNPC5), 1=2, BP1 ) 05577*78 

IF ( aCDELT . EQ. ) GC TO 5260 
HEAD (N1 ) (((KPBF1 



2 3LBFT 

„£3AD (N 1 J ((EPS HA 




IF ( MODELT . NE. 2 ) GO TO 5260 05583*78 

.READ (SI ) {(YGEOW (I.I.J), YTGRGS (I, 1 , J) , J = 1, MNPCS ), 05584*78 

2 „„„„. 1= 2, API ) 05585*78 



5260 CONTINUE 05586*78 

COMMENT - R£.AD REVERSAL INDICATORS FOB STRAINS 05587*78 

..,,„ HEAD (N3) ((IRV(I,1 ,J) ,J=1,MNPCS) ,1=2, MP1) 05588*78 

j30U CONTINUE 05589*27 

COMMENT - ZERO MEMBER INCREMENTAL LOADS 05590*26 

DO 5800 I = 1,HP2 05591*26 

ERX(I) =0.0 05592*26 

ERY I = 0.0 05593*26 

5800 EBsIl = 0.0 05594*26 

IF (INLOPT .EQ. 1) GO TC 6400 05595*34 

COMMENT - PRISMATIC MEMBER WITH CONSTANT F,AE AND AG 05596**8 

PEFT = PRF(ISTT) 05597**8 

PHAE1 = ?BAE(ISTT) 05598**8 

PBAGT = PBAG(ISTT) 05599**8 

DO fa2 ^ I ■ \,V2 05600*34 

S Aii) = 9'2 05601**8 

|| (I = 0.0 05602**8 

|2UL " 0-0„ 05603**8 

i Q A ? = S'S 05604**8 

SQY (I) = 0.0 05605**8 

SQUlj =0.0 05606**8 

ASJI) = PkAET 05607**8 

Fill = PEFT 05608**8 

AG (X) = PEAGT 05609**8 



277 



6200 



b4UG 
b405 



0.0 



CONTINUE 

AE71J • - 

AE JMP2) „ = „0,0 

F 



'(f) = 0.0 

'jflP2) = 0. 

AG(1) = CO 

AGJMP2) = 

2500 



. ANEW) GC TO 6405 
3) GO TO 2600 



6410 

6420 
CQSflENT 

COBHEKT 

COMMENT 

C 

2500 

COMMENT 



GO I 

CONTINUE 

IF (TBESTP .EC 

IF JITYPE .08. 

COXTIHUE 

DO £410 I = 1,ME2 

SX (I) = 6.C 

SI {IS = 0.0 

SZ(l[ = 0.0 

SQX(t) = 0.0 

SQYjI) = 0.0 

SQZ(I) = 0.0 
CONTINUE 
GO TO 2500 
CONTINUE 
" SUBROUTINE NLSS DISC2ETIZES DISTR 
" TSn S 5*TION VALUES OF EESISTIVE SP 

- AND 3PEING STIFFNESS SX, SI, SZ 
ALL NLSS ( LI, JJ ) ' 

CONTINUE 

- STOEE HEHEEE END RESTRAINTS ST1 - 



2600 
COHBZHT 



COMMENT 




COMMENT - ZESC 



COMMENT 
COMMENT 

3290 



3300 
CGKHEHT 

COMMENT 
COMMENT 
COMMENT 
COMMENT 



ST1 

ST2 

SI3 

ST4 

ST5 

ST 6 
CONTINUE 
- ZERO BEBBEE-END-LOADS 

QT1 = 0.0 

QT2 = 0.0 

QT3 = 0.0 

QT4 = 0.0 

QT5=C.G 

QT6=0. 
SET MEMBER END RESTRAINTS TO 1.0E20 

SXM) = 1.0E20 

SY(1S = 1.0E20 

SZhl = 1.0E20 

SX(HEl) = 1. 0E20 

IIJHIi = 1:8118 

PINNED END ROTATION RESTBAIN 
IPINLT .EQ. 1) SZ(1) = 0.0 
IPxNHT . EQ. 1S SZ MP1) = 0.0 
INCREMENT OF t)ISP FOR FIRST 
ERX (1) = 1.0E20 
CALL G5IP2A TO SOLVE HEBBER FOB U 

£S Li ,«l? SI 12 a iaH,SO,H,SL.L3,L4,L6, 
IF fa5.EC.. 5 ) GO TO 3500 
DO 3290 I = 1,21 

SKHT (I) = -1. OD+10 

ML = —1 
TO 9900 

£EX(1) = O.OD + 00 
FORMST HAS ALREADI BEEN CALLED TO 
KHiN PROCEEDING TO A NEW TIME STE 
BUT ONLY TO FGEB INCREMENTAL FIXE 
FURTHER CALL TO FORflLD . HENCE 
COMPUTATIONS DEALING SITE- STIFF NE 



IEUTED HEHBEE Q - W CORVES 
EING FCBCES SQX, SQY, SQZ 



ST6 



IF 

IF i 

- UNIT 



FOR 6 MEMBER SOLUTIONS 



TS 

COLUHN OF STIFF MATRIX 

NIT INCHEMENT OF DISPLACEBE 

«5J 



mm 

05612**8 

05613**8 

05614**8 

05615**8 

05616**8 

05617*34 

05618*34 

05619*34 

05620*37 

05621*34 

05622*34 

05623*34 

05624*34 

05625*34 

05626*34 

05627*34 

05628*34 

05629*34 

05630*34 

05631*34 

05632*34 

05633*34 

05634*34 

05635*34 

05636*34 

05637 

05638 

05639 

05640 

05641 

05642 

05643 

05644 

05645 

05646 

05647 

05648 

05649 

05650 

05651 

05652 

05653 

05654 

05655 

05656 

05657 



COMMENT 

CO K KENT 

C 

3350 
COMMENT 

COMMENT 
C 
C 
3450 

COMMENT 



ALL 



IF TMESTP .EQ. ANEW ) ML = - 1 

IF I TMESTP .EQ. ANEW j GC TC 9 90 
ChLL BEMENI TO FIND INCREMENTAL E 
TERMS IN CNE CCLUMN OF STIFFNESS 

MEMENI f W.F£HI,I6 ) 
DO 3350 KK = f,6 

SariT (KK) = FMMI(KK) 
SET MULTIPLE LOAD OPTION FOR HSMA 

ML • - 1 
UNIT INCREMENT OF DISP FOR SECOND 

E^Y (1) = 1.0220 
ALL GRIP2A ( E fi, RO, i ,Sl, 13 ,L4 , 

ERYM) =0.0 *.#«#*•*« 

AiL ™ -,,=. a ^" i:NI i «.FBBI,I6 ) 
DO 3450 KK = 2.6 ' 

SKMTJKK + 5) = FMMI(KK) 
IF (IPINLT .IE. b 



FORM STIFFNESS MATRICES. 
P, FORHST IS AGAIN CALLED 
D END FCRCES THROUGH 
SKIP THE REST OF THE 
SS FORMATION 





ND-FORCES WHICH ARE STIFFNE 

MATRIX 



INING SOLUTIONS 

CCLUMN OF STIFF BAT2IX 
16,5) 



COMMENT 
3500 



-) GO TC 3500 
ZiiEO STIFFNESS EOS PINNED CONNECTIONS 

SMMT (8) * 0*0 

SBBT 12) =0.0 

SBB'I (13) =0.0 

SMMT (14) =0.0 

saasii5j =o.o 

GC TO 3575 

UNIT INCREMENT OF 



saz(T) 



1.0-20 



DISP FOR THIRD COLUMN OF STIFF MATRIX 



05660 
05661 
05662 
05663 
05664 
NT05665 
05666 
05667*71 
05668 
05669 
05670 
05671 
05672 
05673 
05674 
05675 
05676 
05677 
C5678 
05679 
05680 
SS05681 
05682 
05683 
05684 
05685 
05686 
05687 
05688 
05689 
05690+71 
05691 
05692 
05693 
05694 
05695 
05696 
05697 
05698 
05699 
05700 
05701 
05702 
05703 
05704 
05705 



278 



CALL 
CALL 



EHZi^f 2 ^ ,y n ' 30 ' w ' SL ' I3 ' IU ' I6 ' 5 > 



-MI ( i 

DO 3550 KK = 3,6' 
^ 355 9 SHHT(KK + 9} = FKHI(KK) 

COMMIT - OKI I»CBiHMT_Q| DISP FOE FOURTH COLUMN OF STIFF MATRIX 

CALL *ilmti i §« 5 HO,W,SL,L3,L4,L6,5, 

, e CALL DO 3650^1"= JJ'""'" > 

c^a T -n N xx|pi||^J|» D i SP ^I ( F!U 

.?«£?* i BH 6 BO,W,SL,L3,L4,L6,5) 



COLUMN OF STIFF MATRIX 



3 75 

CCEHEWT 



CCHEENT - 
3800 

CALL 



ERX (MP1) 

_.HB»BKI { W,FHHI,I6 ) 



DO 3750 KK - 

SBMTJKK + 14) = FKMIfKK) 
|| (IPIHH* .L£. OJ GO TO HW 
ZERO STIFFNESS FOR PINNED CONNECTIONS 

SMMT( 6 

SMHT | 1 1 

SKHT(15 

SHHT (18 

SHHTi20 

SHHT 121 
GO TO 9900 
UNIT INCREMENT CF DISP FOR SIXTH 

EEZ(HP1) = 1.0E20 




COLUMN OF STIFF MATRIX 



CALL 
-,N„„ SEKT(21) 

^900 CONTINUE 

ivETHRN 

END 



a!J8f{ i §?& BO '-"'SL,L3,L4,L6,5, 

hebesi ( v. ran. is > 

- FHHI(6/ 



05706*71 

05707 

05708 

05709 

05710 

05711 

05712 

05713*71 

05714 

05715 

05716 

05717 

05718 

05719 

05 720*71 

05721 

05722 

05723 

05724 

05725 

05726 

05727 

05728 

05729 

05730 

05731 

05732 

05733 

5734 

05735 

05736*71 

05737 

05738 

05739 

0d740 

05741 

05742 



:ohh|nt : f" 3 aeT IF. WE dischetize5 "^bee' liheab stiffness data 



co: 
coc_. 

COaKB»X a j L KjMJI||Ag # |*Hl«| gBSpXITB FCECES SQX, SQY, SQZ ARE ZEROED 

XRS( 50). FL( 50). A2L < 50). 

\9) 



coaaos /blocks/ xls( 50), 

2 5XL I 50). 
CO E HON /BL0CK7/ 

2 SZ( 22' 

3 DY 

4 SO 
MI 



\\ 22) , 



sylt 50) , 



SZL( 

AE 

ai 



05743 
05744 
05745 
05746 
05747 
05748 



21 22) , SX( 22) , 

l] 22[; QZ{ 22J; 

nil 22J, ERY( 22?, 

QZ 22 , 01 (22), 



r--^f J ' 302(22, SQZ 22 ; U1( , 22)'/ 
BHlsfh), "Blisfk), m k 2 l\L Ji 11 ' 



S J 
DX 
ER 



Hii; 

M ( 22 2 »' 
05(3,3', 



22) , 



KEEP2, KEEP3A,KIEP3E, KE£P4A,K EEP4B, KEEP4C. KEEP5A. 
KEEP5B,KEEP5C,K|EP5d;kESP6, KEEP?, NCD2 £ NCD3A,' 



COMM 




DC 1020 I = 1,HP2 

SX(I) = 0.0 
SY jl) =0.0 

sz(ij =0.0 



F(I) = 0.0 

AS(I) = 0.0 

SQX (I) = 0. 



1020 



COMMENT 

1050 
COMMENT 



1 + NCDST 



(STIFFNESS AT LEFT OF SECTION) 



_0 

SQxfll = 0.0 

3QZ(I) = 0.0 
CONTINUE 

ICOUNT = 

NC521 ■ NC51T 
Ix GOES FRCfi NC51T TO NC52T 

II = NC51T - 1 

II = II + 1 
READ DATA FROM ONE CARD IMAGE 

XL = XLS (II) 

XR = XRS(II) 

FLT = FL(II) 

AELT = ft EL (II) 

SXLT = SXL(II) 

SILT = SYL (II) 

SZLT = SZL(II) 
If (XR .BE. 0.0) GO TO 1100 

COMM? - RIGHT 6 ol IeCTION? 3 S£CTI0N EEAD 0NE CAB D IMAGE (STIFFNESS AT 
II "II + 1 
XR ■ XRS(II) 
FRT = FLfllj 
AEST = AEL(II) 
SXB1 = SXL (II) 
SYST = SYL (II 



olvio 



05751 

05752 

05753 

05754 

05755**5 

05756*79 

05757*61 

05758*61 

05759*61 

05760*61 

05761*61 

05762*61 

05763 

05764 

05765 

05766 

05767 

05763 

05769 

05770 

05771 

05772 

05773 

05774 

05775 

05776 

05777 

05778 

05779 

05780 

05781 

05782 

05783 

05784 

05785 

05786 

05787 

05788 

05789 

05790 

05791 

05792 

05793 

05794 

05795 

05796 



279 



SZST = SZL(II) 05797 

S8JSSIS3 : $ff?!Ssf a $FIIf§ 3ECII0N SEI STI ™ SS 0N e ^ht equal to ol|li 

"00 FRT = FL1 X22X? 

AEET = AELT g^SX} 

SXRT = SXLT 05nni 

SYRT = SYLI 0580U 

SZET = SZIT nsnnS 

1110 CONTINUE 5§f 2| 

IF (ICOUNT .88. ) GC TO 1210 n^«nT 

COMMENT - FIfiST SECTION OF MELEES STIFFNESS DATA 05808 

XI = TH 05810 

GO TO 1250 nxall 

1210 CONTINUE ?MU 

11 = 12 + 1 81113 
„.. XI = TH - X2 81§J? 
1250 CONTINUE nllll 

IF (X2 .BE. ZL) GO TO 126 otll? 

COMMENT - LAST SECTION OF MEMBERS STIFFNESS DATA 05818 

12 — MP 1 



X2 = 0.0 



05819 



GO TO 1270 " n^fl9l 

1260 ZI2 - XB/TH +1.0 0°5822 

I* - 4J.<: ORfl?'? 

1270 Nfl = 12 - I1* Tfl * TH °5824 

COMMENT - SUBROUTINE LINSTF DISTHIBUTES F AND AE 05826 

CALL LINSTF ( FLT, FBI, ?, FTT2, LI ) 05a?7 

CALL LINSTF AELt| AERT, Is, AETT2, L1 ) 05828 

COMiJENT - SUJ3EOUTINE LIKLD DISTRIBUTES SX.SY.SZ, QX,QY, AND QZ 05829 

IF (SXLT .BO. 0.0 .AND. SXRT .EQ. O.of GO TO 1280 05830 

CALL LINLD ( SXLT, SXET, SI, 11 ) ' 05831 

U8 ° „ I* ( 3J I- T »SQ. 0.0 .AND. SYRT .SQ. 0.0) GO TO 1290 05832 

CALL LIKLD ( SYLT, SYRT, SY, L1 ) 05833 

,2y(J „„,. IF ( SZI '' 1 «2Q" 0.0 .AND. SZHT .EQ. 6.0) GO TO 1330 05834 

1330 CALL CONTINl^ INLD ( SZLT ' SZBT ' SZ ' ^ ' 05835 

1330 CONTINUE _ 05836 

1385" " !f T 5M 3L ^ikPaSMS ?SI8 C4aD 1F IX LESS THAN NC52T llli 

* 900 fl ziu£r iNUE §111? 

END 05842 

gftHfii : iSBSSFI.^iSHll fiV&S 1 * ) IREAB Vi8IATI0SS IN " KE > S ff|| 



DIMENSION ST (11) Udo4o 

COMMON ^p; N |t,X^X1,X2 H,TH,HSQ.ECa,X2L,I1,I2,N Q ffjf 

T - FIRST SECTION OF MEMBER ^nSn 



COMMENT - iinji. jiLiium ui nancBti 

STT2 — 1 05851 

1150 CONTINUE nlif 2 

IF ( Sl'E .EQ. STL ) GO TO 1310 n?nia 

COMMENT - LIHSA2 STIFFNESS SECTION SifiS 

COMMENT - CALCULATE SLOPE OF LINEAR STIFFNESS VASTATION 05856 

,-,.....„ „ DS = ( STE - STL)/(XR-XL) 05857 

COMMENT - FIRST ELEMENT (TH LONG)" OF SECTION 05R5R 
Co'SSfll I ^f^^If^F STIFFNESS OF ELEMENT CONSIDERING JUMP AT 

STA = STL n5flft1 

STB = STL + DS*X1 0586? 

STT1 = 0.5*(STA * STB) 05863 

IF (NO 1 4c' /™* S ?T1*STT2)/(X2L*STT1 ♦ XTSTT2) 05864 

IF (NO .EC. J GO TO 1250 05865 

iipncViiVnc gill? 

COMMENT - REMAINING NO ELEMENTS n5flfiR 

coum - ^fSJS.P^ffl/lJg P01NT 0F ELEMSKT gfill 



STA = STB 

STB = STA + DS*TH 



05871 



1318 continue 1 ' -«.*<«*♦«■) 5 7 7 | 

STA = STB n^fni, 

STB = STK n5ft7fi 

,-.„ STT2 = 0.5*(STA + STB) 05877 

1290 GO TO 1800 SHI 

COMMENT " DNIFOSa STIFFNESS SECTION n5fl7Q 

COMMENT - FIRST ELEMENT (TH LONG) OF SECTION n5RR0 

COMMENT - START T 0F E SECt1oN E 3IIFF;,ESS 0F ELEMENT CONSIDERING JUMP AT 05881 

1310 " STT1 = STL nSfiqT 

r. ,>, Sr(I1 > S (TH*STT1*STT2)/(X2L*STT1 + X1*STT2) 05884 

IF (SQ .EQ. ) GO TO 1360 ' 05RR5 



I1P1 =11+ 1 



05885 
05886 



COMMENT - REMAINING NQ ELEMENTS HAVE CONSTANT STIFFNESS 05888 

DO 1J30 I = I1E1, I1PNQ 05889 



280 



till my- u iL o5 t 9o 

COM "Ii.;iia! Sfi*8 t [rii.8Sf alB8 *" "• SY - sz - QX - QY - AND * z II 

DIS'NSIOH Q(L1) UDtty/ 

CO a , £N 5 C ^P^ K kc||'^^l S Ii £s AHI,TIO§' TH ' H3Q ' flCU ' X2i ' I1 ' I2 ' K = l|f 

IS : Sffi^#^s&HB3UM*n»»^fi™ III 

3l = Qfi - DQ*X2 



IF ( QC 
IS \ QC 



05904 
05905 

= 31 + S 2 "" 05907 

lt. o.5 ) qc_= rQ c_ _ 8iIos 



.LE- 1.0E-1Q ) GO TO 1005 05909 

ll if * 5c cc*ld -f Q i: r ir l Q?"ii°) To 1005 

COMMENT - SASE AS ABOVE FCR ELEHENTAT LEFT END OF SECTION 05916 



wx - j^m. - W*J 05911 

IF | QC .if. 0.0 }.QC_=_ r QC 

CONLD 

SiiiE AS ABOV 

1005 01 = £L 



Q2 = Hi + dq*x1 ns9ift 

QC = 1 + o2 Sillg 

IF gc -LT- 0.0 ) qc = -qc Si|4l 

U ( QC ,LE. 1.02-10 ) GO TO 1009 05971 

iV* U^^r^T 3 * 02 + 2D/(Q1 + Q2) 05922 

QC = ^ b * x1 *l°- 1 + ^ 2 ) 05923 

: .LT. 0-0 ) QC = -QC 05925 

^ IF < x Q x i«fa 2 xi G ° T0 285 ° 

COStlENT - SAflE AS ABOVE FOE R2BAINING NO ELEHENTS 05930 

' 1 ' N0 - 05931 

05932 

+ DQ*TH 05933 

+ G* 0^934 

0.0 ) QC = -OC 05935 

QC ,LS. 1. OE-10) GO TO 1990 05936 

5y = - X $yV^ /3 - 0J * (2 -°* Q2 + SD/(Q1 + Q2) 05937 

XX - XX + TH OSQ^ft 

QI = 0.5*TH*(Q1 + Q2) 05939 

CA " „,„ T CCNLD ( Qi" Z, Q, L1 ) 05940 




1S90 CONTINUE 

2000 CONTINUE 



05941 
05942 



*2™ OB955 

END 05944 



******* *************************** SUBROUTINE ********************************* 

SUBROUTINE CONLD ( QI, Z, QO , L1) 05945 

CLIENT - SUBROUTINE CONLD DISTRIBUTES CONCENTRATED VALUE CF LOADS, 05946 

SRSSI8E " IS5J5J?* STIFFNESSES, AND RESISTIVE SPRING FORCES TO ADJACENT 05947 

C0&H2ET - STATIONS I AND IP1 05948 

IMPLICIT KEAL*8 <A-H,0-Z) 05949 

DIMENSION QC(L1) 05950 

COBHON /BLK2/ XL,XR,X1,X2, K, IH ,HSQ , ECU ,X2L , 11 , 12, NQ 05951 



05952 



Zl = Z/TH * 1.0 

I = ZI 05953 

ZZ = Z - I*TH + TH 05954 

IP1 = I + 1 05955 

QC (I) = QO(I) + QI*(TH - ZZWTB 05956 

.,..„„„ SO(lft) = Q0(IP1) + QI*ZZ/lfe' 05957 

Hl 0aS 05958 

END 05959 



********************************** SUBEOUTINE ********************************* 

SUBROUTINE NLSS ( L1, JJ ) 05960 

S9SSI8S " SUBSOUTINE NLSS DISCRETIZES DISTRIBUTED MEKBES - » CURVES C596 1 

COflKENT - TC bTATICN VALUES OF RESISTIVE SPRING FORCES SOX, SQY, SOZ 05962 

COaHJiNT - AND SPRING STIFFNESS SX, SY, SZ 05963 

IMPLICIT £EAL*8 (A-fl,C-Zl 05964 

DIMENSION DC(3,3) ,DCT[3,3) ,WT(3) ,KTT(3) ,FT{3) ,FTT(3) 05965 

COaaON yBLOC'h/ tisi iff, dM'251, ZLSt 2S), 'dc1S( 25), 05966*42 

i S^S,|?'» SfSi.^if PRAE(25), QH< 25), «n{ iS). 05967*42 

3 Pi'.AG(251, =.LEf<N (25i, 05968*42 

* 5??9*i e ? i »' 5IIFM,i?J» I?IN5( 25), NC51f 25), IHLOPj 25), 05969*42 

3 NAl( 45), &S2L{ 25), HSIL{ 25), N3ZL( 25), NAE( 25), 05970*42 



•I?. HA. if 1 1- ill. 



281 



1*42 

05973 
05974 



b f ;. f ; 4 • Hi Si KKfi-ai. f 



2 



s 8 

6 xAE-AN, IFORK, NM, NJI. NST NLT H ' Ki^Ii 

* mop! . liisfj {llitfl: ■««f»i:18|: Slll,(!i':!Sl- gffft 

IF (IAXOPT .20 1) Rrt t? *>mn 05987 

COMMENT - TRANSFORM MEM% LlSP 1C STRUCT COORD FOR IAXOPT = 2 ollii 

Dc(2,i| = °:8 05990 

DC 3,1 = 0.0 "991 

DC (3.21 =00 05992 

ocln,3) =oo 05993 

DCT2 3 = °599« 

DCT{3,1) = 0.0 Scllf 

DCT(3.2l = 05996 

DC (J 31 = 10 05997 

DCT(3 31 =10 05998 

Wli'\l m CCli(ISTT) ° 06 5999 

DCJI 2 = DC(1. ( f 2) 06002 

DC? (1,11 = DC (1,1) 06003 

DCTh;25 = DC 2 1 9§%W 

DCT|2,1) = DC 1 2 9^005 

DCl|2,2{ = DC 2 2 S?226 

FT 3 = olo 06 °08 

DO 1300 l I = 1 EP1 06009 

COMMENT - F ISO A| USED jj| TEKP STO& FOR DX AND DY ONLY IN THIS SOB 06011 

Uth « Diftj 06012 

CALL KATM31 (tct.H j X) |jjj 

Dili} = KTT{2J 0|017 

1300 CONTINUE nen , Q 

^100 CONTINUE 81853 

COMMENT - AXIAL RESTRAINTS n£°io? 

DO 2200 I = 1.MP2 ntnll 

--,.-.■ SQX(I) =6.0 osn 22 

2200 SX(I) = 0.0 cstnol 

.,.," (NSXL(i3TT) EQ. 0) GO TC 2300 g|§lg 

CALL NLSNEJ. (S X.DX ,S C X ,L 1 NSXL (ISTT) NSXR (ISTT) , QM (ISTT) , 06026 

2300 CONTINUE ^ (ISTT) , WRXM, WHTXH, W, 1 ) 06027 

DO 3200 I =_1,MP2 lloll 

3200 ISyp-'o.V gf gf 

IF (NSYL(isTT) .BO, 0) SO TO 3300 06032 

CALL NLSNE* (S ! f BI.SQY . II -SSYL (ISTT) NSYE (ISTT) ,QH (ISTT) , 06033 

3300^ CONTINUE " (till) , «R*&, rfRTYK, j3, 2 ) 06034 

COMMENT - ROTATIONAL RESTRAINTS nsnli 

00 4200 I = 1,HP2 Rf 23§ 

502(1) = 6.0 ntnVa 

4200 S2(fl '- 0.0 SfiU 

IF (NSZi(ISTT) .EQ. 0) GO TO 4300 06040 

,300 2 ONTINU ffii^f^tfSWftJIC'^PP"! ^(ISTX) ■ 818*2 

ft «ftj° »f i"^ G ° TC 5 ^° gfoSf 

COHHSKT - RETU3N DX AND DY TO KEMEER COORD OfiOUfi 

Dy|i] - Sift, 06 04 U f 

CC13E.JT - TRANSFORM 3 QX aVsQY TC MEMBER COORD 06049 



06050 



;t(ij = sqxjii 

CALL ««|lj(fcyjgfl 8IS15 

SOY T - m 06053 

5100 COBXISOB Q ( 3 ~ ' 2i 06054 

5400 CONTINUE 81x11 

RETURN RcRct 

END 06057 

£NU 06058 



282 

ill : iiiiMijiioiiPiiiiiS::: — jb 

COMHMl - AND ROTATIONAL SPRINGS S "FFNESS T0 KLSS FOfi AXIAL< LATEPAL 060 g| 

COadEN I«PL!c !TilI^* L i A ^l 6-l) NELA3TIC """DIM ALGOSITH* IS USED 8f8t# 

DIK2NSIGK SXYZfLI) , DXfzfl'l) snYV7nn 06066 

DIMENSION lfSfl(il,1fi), aEiH(ir?0» ( } 06067 

2 CM %w^ fei \$.m%.**immi V . «H(2o t ii, f gig?? 

CGfiSOH /BLK1/ T01. ELEHNT, NJST KEEP3r Hrmr 06072 

| J*? AN . IFCEfi, NH, ' NJT.' NSt' NLT ' £ TYPE ' 06077*61 

COM fl ENT - KOFFQW^ IN EFFECT SETS NO LIMIT ON D E FOR«ATION g|g|i 

NPT = NPiaJNSL) 06084 

COKBEHT - DO FOB EACH e£ePENT ' ' 8 » TH ' KWMI ' SMAXBI, STEEP ) 06090 

DO 2600 I = 2 7 III 06091 

DO 1300 J = 1 ' NPTM1 06092 

B(J) = £SSI(I,J) 06093 

130C CONTINUE JJJW " ■"*&*) Hill 

SUS : ifAX?I11ilf'iI||^ I ii£ A ^IIf|I AS AVERAGE OF ADJACENT |lfl| 

DO 1400 J = 1 , NPTH1 °A\ Q n \ 

1400 CONTINUE WiUfl(I ' J > " SI < J > 06108 

SQXYZjI-1) = SQXYZ(I-T) + 0.5 * QJ nfilin 

2600 CONTINUE ^ " » " SZYZ » I ♦ «« • S! f 

RETURN 8§1H 

8ii 1: ?i 

CDJiiiEST -SUBROUTINE aSECDB UTILISES THE iiflBls-Sntffltl ?flvf^ p ' Of JJ 1 2 

COMMENT - 4T THE ENDS OF THE BE«3ER TO CREATE (LINEARLY I HtHIoLATEDI Sfilll 

2 COaH M^ V JSS§J,??>' IS *< 2 °>' "Q H (20.n,, 5M(20 r 11, f 06ll2 

nr 1 tin 7 — -i t* Tl( A ^ 



DC 110 J = 1,NPT 



rQQS (1 1) ,WHE(1 1) 06124 
06125 
06126 



QQL(J) = NQM (NSL,J) n£l?n 

qCHfJi = NQ«(NSR^J) nli^n 

««'k{j) - ssa nsr,j ,1! J 19 

110 CONTINUE ' xfHl 

A JS = M <J o I J 2 

IP 1 =' M + 1 06133 

DC 1000 I = 2,HP1 06135 

DO 150 AL WlJpi AI ' 1 '5) /A« Mjlj 

gfl (■?) ' JPCLjJl + ALPHA+(aQS(J)-QQL(J)) ) * QMT * TH 06139 

150 CO*TINui j| = (5SLW * *I.PH»*l«BHljJ-SgLlj{j j * S«T 06 140 

STEEP (1) = QQ(2) / W«(2) SfJSJ 

NPTH2 = NPT -2 fifliii 

NPTB1 = NPT - 1 SfVSS 

IE ( NPTH2 ,BQ, ) GO TO 205 Sf 1 ,^ 

DO 200 J = 1 , NPTH2 ncinc 

5L0K = ( C'Q(J+1)-QQ(J) ) / ( awf J+1) -8ft (J) t fi5 J? 

SLOKP1 = ( £ 2 {jt2W<J + 1j / ; { « ) (j:5j ( -U , (a+1) ) 06148 



6 



283 

205 CCNTINDE 06151 

DO 220 J = 1 ipiai l ' 0|15g 

WWHIfl.Jj = UH(J+1) 06155 

1000 CONTINUE 06158 

REXOiN 06159 

END 06160 

06161 

DIMENSION (MO) , fiaAXMO) , DHMOJ DBTMOl 2§lfl 

CCMiiCN /BLKT/ TGL. ElHnT NJSt' i?ip^f- »rn5r 06 167 

jgfe: 5§88j* jsk- g««: |g|f»: fffii. gg|: § | j:j 

& iaban, xforIi, n«, njt; nst' hlt ' i TrpE ' 8!f?l!f 

7 co KflON Aih, iHkii^i t ii R * "»«.»!: N% L | B« 

COaBOH ^SKT1< / IHTjipfNSfJ ' N * FO«OLD(50,6,, 8f »3 

COAflOH /SK1 15/ JJ ' ITA?E ' N3 06179 

COBflON /SKT18/ NCHECK 21119 

COMSOH /SKT20/ BCRGCN f 2 1 . 3) , MC02EV 12 1 11 9^3§J 

COMMON /SK222/ TIME, Jl li&tfl I2STEp'r7i» 2111? 

Illlllf : i||f g s fhssife5i ill ki i" » ^yisssiif «■ 

§815I8i : SSI iy85l!;F SifSSiYI^ff!,- J#sIiA§T a ll^If 

S = 0. 06188 

BK =0.0 061 ^9 

DO 2200 K - 1.NPTM1 °<?190 

IF ( ll^ , £ B I 5 2St )/,, ' R ' ( H(K) " 5 - 0D - 10) > GC T ° 1500 8HI5 

IF , fcHEcTfL! I f SoWaio gill! 

" I * .HE. 1 i GO TC 1450 RfJlS 

GO TO 2000 2§ 199 

1450 CONTINUE 06200 

„„ UHI(K) = OP(K) 2§?2o 

IF IFAE .Eg. 1VG0 TO 1460 8W9| 

IF ( K .BE. 1 GO TC 1460 nl$nl 

.,,,„ KCfiGCN(I,MCXiZ) =0 81382 

1460 CONTINUE 06205 

GC TO 2000 06206 

1500 CONTINUE 06207 

IF ( U .ST. tJfi(K) 1 GO TC 1600 8I22| 

Z = - RMAX (K) Uo^uH 

IF j NCHECK .BE. 'l ) GO TO 1550 olli? 

IF ( K .BE. 1 GO TO 1550 nJoM 

IF ( MCRGCN(I,MCXIz[ .HE. 1 ) GO TO 1550 2» n 

HCUBEV {I,HCXIZ) =1 ' nt?!?, 

.„„ GC TO 2000 nciic 

1550 CONTINUE 2I?1I 

„_ , UET{K) = U + H(K) S?2 S 

IF I IFAE ISO, II GO' TO 1560 §|§U 

IF { K .82. 1 j GO TO 1560 RfiJg 

,-,„ HCBGON(I,HCxtz) = -1 SSfJS 

1560 CONTINUE ' 21139 

GO TO 2000 2£??1 

1600 CONTINUE 2§3 22 

Z = BHAX(K) 2???2 

IF ( NCHECK .BE! 1 ) GO TO 1650 ns? 2 ^ 



IF J NCHECK .BE; 1 1 GO TO 1650 bW* 

IF { K .HE. 1 GO TO 1650 c,eMl 

I? X Hcif^ ( ii a ixxL*I E r 1 ' G ° T ° 165 ° °62 2 2 2 7 

GO TO 2000 (I ' MCXYZ > - ' 06228 

1650 CONTINUE 0S229 

UET (K) = D - W(K) 2133? 

IF ( IFAi ,EQ. J ) do TO 1660 2f?Jl 

IF { K .ME. 1 GO TC 1660 8§|?| 

,,,- KCHGOH (I,MCXYZ) = +1 nl$\l 

1660 CONTINUE 06234 

2000 CONTINUE 06235 

j, = e + 7 06236 

2200 CONTINUE 06237 

IF ( IT¥P£ .GE. 3 ) GC TO 2210 6 2 3 I 



284 



II loilo ;i8: l ^-"MiiU, ..Q. 1 > GO TO 2220 figlM 

2 210 CONTINUE 06242 

rI?J.I5 D ?S -EQ. 1 ) GO TO 2220 SI 2 !};? 

U TO !!lo T) • EQ * 1 • AND - NITF ' EQ " 1 ' AKD - NITEBH(JJ) . EQ. 1) GO TO 222006245 

2220 CONTINUE 06246 

IF ( |COH E! (I £ HaYZ) .EQ. ) GO TO 2250 81131 

IF f ITYPE .LB. 2 ) GO TO 2240 Itoll 

tH,L£ SI>th ' E 2- 1 ) GO 10 2250 nt\V\ 

2 IF u4s S3S fe^rf'gfiiiif D iT F * EQ ' 1 * AND * NITEBa (J J > - EQ - 1 » °"s2 

GO TO 2250 ' ' ' 06253 

2240 CONTINUE 06254 

2250 cSntinoe-" * EQ - ° > actJB ^(x,«cxrz) = o Still 

IF ( ?SS E S§ -»E- 1 ) GO TO 2800 St§§7 

2800 COHTIHU?"* = IBTH3E * KM«<I.HCm) Slsll 

RETUBN 06260 

END 06261 

06262 

+ ****sa^^;orGEiP2r:rrrsn3 3 ^ E 2 s aTi «r E **">♦"«♦*****♦♦******»*«**+*♦* 



IMPLICIT KEAL+8 (A-H,0-Z)~ ""' KISS?* 90 

DIMENSION CfL6,L<h,B(L6),X(I6) SIlf§.-,o 

co w ag^gisi'^-ft^ SHII 

COJiaON /SKT15/ JJ 0&269 

999 FOMAT f//;J|^' F ffl§gI F f„ 50llT 3 S0t^I0N,/, §|^ 2 

2 0iI x * K*IIfi<» 8H CCEFF =,1PE13.6,//) ' / ' §^274 

N=NL 06275 

co HaE ^ A i L F o F is^ D ( ii 3 I fi I x K ^^' L6 ' B) Still* 73 

„ HB1 = N - 1 06278 

DO 98 J = 1,KH1 06279 

JM=J+H 06280 

IF (J» .ST. N) JH=N 06281 

-r^ - , . 06282 

J?1 = J+1 „,„, 

aa=K+i Sf 233 

IF ijltj ,GT. N) HB = N-J+1 nfi9»S 

DO 97 K=JP1,JK nfMl 

KK=K-JP1+2 nf 2 §3 

IF (C(J. 11.GT.0.0 ) GO TO 50 nllll 

IF I KFSUB .EQ. 22 ) GO TO 30 2? 2 |§ 

PHINS 999, J, C?J,1) ' nzoon 

GO TO 40 ' X? 2 2? 

30 CONTINOE R£ 2 oo 

;ia PKINT 883, JJ, J, C(J,1) SI 29 , 2 

40 CONTINOE ' ' nloan 

.1=10001 06|94 

GO TO 195 06295 

50 COEPF=-C(J,KK)/C(J,1) X?^ 6 , 

yKj-BJK)i&02PF*l{J) 8111s 

DO lf E !-i E §M ' 1) S ° T ° 9? 06300 

II-I+K-J ° 6301 

96 CONTINUE C <^> =<= <K,D 'COIFF* C ( J, II) jjjjjj 

97 CONTINUE 06304 

98 CONTINUE UcJUb 
C0 3.HENT - BACK SUBSTITUTION ?c!Rt 

IF (C(N, l),3T.0.O } GO TO 110 filial 

IF ( NFSUB -EQ- 22 ) GO TO 100 nfi=»nq 

PHIN'± A 999, N, ClN,1) ' oHIa 

GC TO 105 ' SflJ? 

100 CONTINUE n'iU 

PfiINT 888, JJ, N, C(N,1) P,?^ 12 

105 CONTINUE nlliu 

3=10 001 6314 

GO TO 1 95 Uojl b 

110 !^ = B<H)/C(H,1) SlIlT 

D ° 'Tn-KkJi °"l9 

IF (KK -GT. S) GO TC 150 nfiT 2 ? 

NM=NM+1 nAT?4 

GO TO 160 °6322 

, 1 ?0 NH=M nllifi 

HW2 — K ^^ "^ ® 

DO 170 11=1 NM llWa 

NN1 = NN1 + 1 nfil 2 q 

NN2 = NN? + 1 UDJ 2 y 

™" NN<i + ' 06330 



285 



170 CONTINUE* = X(K) ~ C(K.HHI) * X(NN2) 

190 CONTINUE X < K >= X <K)/C( K ,1) 

195 CONTINUE 
RETURN 
END 



nm 

06333 
06334 
06335 
06336 
06337 



SS3HH : Poi B uh c ol L s L3 '"BWSi^i&ia&noM and fsob 22 for HEHBE8 

IMPLICIT BEAL*8 (A-H.0-2) 
COMMON /BIK5/ &FSUB,NITF,N1,N2 

JiIi!:l;Illilllii!;flia : '!Sf"i 

END 



******** ************************* 

06338*72 

06339 

0634 

06341 

06342*72 

06343 

06344 

06345*72 

06346*75 

06347*72 

06348 

06349 



*****rDBHSoTi«ris*SB2rrr«r*ri6 so !5 oo ? i HB NE , + **********^********** 



COMHEKT - MATRIX as AND LCAD MAT SIX HO 
IMPLICIT HEAL*8 (A-E/O-Z) 



OF SYflMETBIC STIFFNESS 



DIMENSION Ha(I6,i4);&0(LB) 



2 PHMJ3) ,FSS(3l,faM3 l 

COMMON /BLOCK 1/ X(25\. 
2 Q2Z(25), SXX[2 5), 

"YY(25f. DZZ(2 5[' 

SXi(25 . EBYY{25), 



J DYY (25( 

4 EEXX(25 

5 NSXX(25 

6 HSYPJ25 
COMMO 

2 B.. 

COMMON /BL 



DC2 S i 
PRAGl 
IOPOI 



DZZ 

EBI?(25) , 
NSYYJ25J , 
ISTJR(25) 

. »2BI 

2/ DXS( 25) , 
PfiFf 25 

ELEKN 
IPIKL 



SYY(25) , 
EXXl255.' 
EflZZ(25) , 
NSZZ(25 , 



QXX (25 
SZZ/25 
SYY(25 
QMJ (25 

lMJ(25 



QYY(25 
DXX(25 
SZZ (25 
WHJ (25 
NSX?(2 



SVV(25), DVV(25), 



ZLS( 25) , 
QH( 25), 



si: 



23 



oif UOI . XSTJB 

N /3ALA0 1/ 2W(2 

"(25), ' NsW( 

H /BL0CK2/ DXS( 

]25)' ELEri 
P( 25), IPIK^ 

NAL{ 25), NSXLf 

NSXfi { 25f, NSYE( 

COB HOB /kocfcV DXL( l 25r, 

2 DC2L 25) , UQX( 25l' 

3 NC61J 25j; iovMatlsf 

COHHOg /giOCH/ FOMM(50,6), 
2 JT1 (50) - JT2(50) ' 

COMMON MoC10/ SSL (4,24) 

COMMON /3LK1/ TOL, ELEMNT. NJST KFFPir jrmr 

KEEPJ, KEEP3A,KEEP3E,KEEP4A,KEEP4B:KEEi4C K^EPSA 
KEEP5B, KEEP5C,KESP5D' KEEP6 , KEEP7 . C 2 T"" 
VC93B, NCD4A, NCD4B.'NCD4C HCdIj ! Srnq& 1 



f, 

ESVV(25) , 



DYS( 25). 
P8AE( 25f, 

I 2S/, IPINB( 25), NC51( 25), 

NSY1( 25) , 
HSZfi( 25) ' 



DYL( 25), 
UQT( 25) ', 



NSZL( 25) , 
NCDS( 25) , 



ZLL( 25l',' 
NCD£( 25), 



fS * c PiU 2 dti z . s * im 



DCISf 25) , 
HM( 25)/' 

INICP( 25) , 

NAR( 25), 
IAXOPS { 25) 
DC1L( 25), 
IAXCPLf 25) , 



-»w, , 11(50), 
IMH(50), IMC (50) 



3 ^£ii^3B,KE£P5C,KE2P5D, KEEP6 *K EP7:'ScD2 '~'£rn3»"' 

5 NCD5D' K A ' £S# fl ' ?iS 4C ' PP* SCD5B, NCOS*: 

7 COMMON A P K5/ NFS ? oi, XXI ^,H2 LTT: *^^ ^TL 

COMMON / RI / NL, fl£, J1 ' 

COMMON /NIT/ APROB 
2 CO HH OH /SKT14 / 1^21 2.1QJ. iTftpE FOMOLD(50,6>, 

4750 S8SS2! ffi;S0( 1 PEf^I)° I ) (25) ' EEYYoL(25) ' ££ZZOL " 25 )^B7VOL(25) 
DATA PRINT /4HRINT/ 
NL4 = IfL 
ML4 = RL 
DO 6000 JIN=1,NJT 
IF (JTN .NE. 1 ) GO TO 1300 
SET CONSTANTS fe FIRST CALL FROM GBIP2A 



COSMENT 



IHBP1 



IHB 



COMMENT 

1300 
COMMENT 



1400 



IHB1 = IHB 

DC(1,3 

DC{2,3 

DC (3,1 

DCJ3.2 

DCT ( 1,_ 

DCT 12,3 

DCT (3, 1 

DCT(3,2j = u.u 

DC(3,3) =1.0 

DCT (3,3) =1.0 
COMPUTE TBE EQUATION 

J1 = 3*JTN-2 
ZE20 SSL AND FSS 




NUMBER 



DO 
DO 



1400 I 

1400 J 

SSX 

FSS 

FSS 



■ 1# .3 

1,IBB°1 
) = 0.0 
= 0.0 
0.0 






********** 

06350*72 

06351 

06352*74 

06353 

06354*72 

06355 

06356 

06357 

06358 

06359 

06360 

06361 

06362 

06363*70 

06364*75 

06365*42 

06366*42 

06367*42 

06368*42 

06369*42 

06370*42 

06371 

06372 

06373 

06374 

06375 

06376*75 

06377*79 

06378*61 

06379*61 

06380*61 

06381*61 

06382*61 

06383*61 

06384 

06385 

06386 

06387 

06388 

06389*75 

06390*72 

06391 

06392 

06393 

06394*72 

06395*72 

06396 

06397 

06398 

06399 

06400 

06401 

06402 

06403 

06404 

06405 

06406 

06407 

06408 

06409+72 

06410*72 

06411 

06412 

06413 

06414 

06415 

05416 



286 



COMMENT 
COMMENT 



COMMENT 
COMMENT 



HPi»P;ii»«°° BW1H "J."B!P.{B.J«Jfci I " 

(_JT1 (JJ^NE.^ JTN .AND. JT2(JJ) .HE. JTN ) GC TO 350 



I5TT 



-ST(JJ) 
SKIP FOE mil MEMBER 
IF ( I5TT , EQ. ) GO TC 3500 

TEANSFCBMATICH MATfilS AND ITS TfiANSPOSE 

jgi : |if i?UKw 



DC} (1, 

DCT (1,2) 
DCT(2,1) 
DCT (2,2) 



DC(2, 1 
= DCM,2 
= DC (2, 2 



COMMENT 



IF ( JT2(JJ) .EQ. JTN 

- FORM SMS FOB MEMBEH WI 



COMMENT 
2250 



2300 
COMMENT 



COMMENT 
2350 . 



SMM 
SMH 
SMM 
SMM 
SMM 
SMM 
SMM 
SMM 
SMM 
FOBM EMM 
FMM 
FMH 
FMM 
GO TO 25 
CONTINUE 
FORM SMH 
SMM 
SMM 
SMH 
SMM 
SMM 
SMH 
SMM 
Sflfl 
SMM 
FKM 
FMM 
F_ 
FE 



= SHCJJJ,2 
= SMC JJ,3 
= SMC JJ,2 
= SBC i J J, 7 
= SMC JJ,8 
= SBCiJJ,3 
= SHCiJJ,8 
SMC?JJ,12 



GO TO 230 
B FBOB JOINT AT JOINT JTN 



IITH F 



- Fosa 



2500 CONTINUE 

COMMENT - TRANSFORM SMM ABD 

CALL MATM33 ( DCT, SM 

CALL MATM33 ( T33, DC 

2550 CALL MA1H31 ( DCT. FM 



FOB MEMBER H_ 
;i) = FOMfl(JJ,1) 
,2} = FOMM{JJ,2) 

3) = FOMM(JJ,3) 

FOB MEMBEB WITH 
= SMC JJ,16 
= SHCl'JJ, 17 
= SHCl'JJ, 18 

= saciJj,i7 

= SHC|JJ,19 

= SMC (J J, 20 

= SMC|JJ,18 

= SMC|JJ,20 

= SMC (JJ,21 

FOB MEMBEB BITfl 

= FOMH(JJ,4 

FOMH{JJ,5 

FOMMjJJ,6 



BOM JOINT AT JOINT JTN 



TO JOINT AT JOIST JTN 



flB HUH 
'SH(I) = 
MM (2) = 
MM<3) = 



TC JOINT AT JOINT JTN 



COMMENT - ADD 



COMMENT - ADD 



COMMENT - Si 
IF 
IF 

COMMENT - FOE 



SMM 
SMM 
SMM 
SMM 
GO 
COMMENT - FORM SMH 



(SOBTBACT) IN 
FSS(1) = FSS 
FSS (2) = FSS 
FSS (3) = FSS 
IN SMS TO DIA 
SSLM, 1) = S 
SSL 1,2 = S 
SSLM, 3/ - 5 
SSL(2,2) = S 
SSL(2,3i = S 
SSL(3,3) = S 
IP FOR SMM BSTC 
JTN .GE. JT1 
JT2(JJ) .EQ. 
SMM FOR MEMB 
SMM( 1,1) = S 
SMM (1,2) = S 
SMM(1,3) ■ S 
SHM(2,1) = S 
SMH(2,2) = S 
2,3) = S 
3, 1) = S 

3.2) = S 

3.3) = S 
C 3000 



„ FH 5„?f STROCTOHE COORDINATES SMS AND FMS 
, SMS) 

§\BS TC STBUCTOBE LOAD MATRIX FSS 
1) - FHSMl 



- FMS(2 

- FMS(3 
AL SDBMA 



SL(1,1) + 

SL(1,2) + 

SL(1,3 + 

SL{2,2 + 

SL{2,3 + 
SL(3.3 



SIMMETBICAL TEEMS 



SIX OF SSL 
SMS(1,1) 

sasi 1,2) 

SMS(1,3) 

SMS{2,2) 

SMSi 2,3 
^u^^,J) -r SMSi3,3) 
H ABE TO LEFT OF DIAGONAL 

[J A\ fiS-ig^S 1 ' JT2(JJ) ] G0 T0 350 ° 

EB SITH FBCM JOINT AT JOINT JTN 
HC(JJ,4) 

-\jj;5 

'Jj,9i 
- JJ,10) 
MC(JJ,11) 
MCfJJ, 13) 
AC JJ,14 
MC(JJ, 15) 



HC 

ac 

HC 

HC 



2700 



SMM 
SMM 
SMM 
SMM 
SMM 
SKM 
SMM ,, 
S3M (3,2 



for member bitb 
;mc(jj,4 
;mc(jj ' 
;mc(jj 



i,i) 

1,2 

1,3) 

2,1) 

2,2} 

2,3) 

3,1 



ID 

•I, 



S 

= s, 

= s, 
= s 

= s~ 

= smc|jj, i» 

= sr _ 
s, 

s; 



TC JOINT AT JOINT JTN 



5MC }JJ,5) ' 
>MC(JJ,10) 



MC(JJ,6) ' 
MC(JJ, 111 
HC(JJ,15 



SMM(3,3) = 

3000 CONTINUE 
COMMENT - TRANSFORM SMM TC 
CALL HATH33 ( 
CALL MATM33 ( T 
COMMENT - PLACE SMS IN S_ 

J21 = JT2(JJ) 
J21 = IABSJJ21) 
I5TP = 3+J21 + 1 



STEOCTDBE COORDINATES SMS 
CT, SMH, T33 ) 
33, DC, SMS ) 

JT1 (JJ) 



06417 
RIX 06418 
06419 
06420 
06421 
06422 
06423 
06424 
06425 
06426 
06427 
06428 
06429 
06430 
06431 
06432 
06433 
06434 
06435 
06436 
06437 
06438 
06439 
06440 
06441 
06442 
06443 
06444 
06445 
06446 
06447 
06448 
06449 
06450 
06451 
06452 
06453 
06454 
06455 
06456 
06457 
06458 
06459 
06460 
06461 
06462 
06463 
06464 

06465 

06466 

06467 

06468 

06469 

06470 

06471 

06472 

06473 

06474 

06475 

06476 

06477 

06478 

06479 

06480 

06481 

06482 

06483 

06484 

06485 

06436 

06487 

06488 

06489 

06490 

06491 

06492 

06493 

06494 

06495 

06496 

06497 

06498 

06499 

06500 

06501 

06502 

06503 

06504 

06505 

06506 

06507 

06508 

06509 

06510 

0651 1 

06512 



287 



SSLM,ISTP) 

S3L(1,ISTP * 
SSL (2, IS rpi 
SSL(2,ISTP + 
SSL(2,ISTP + 
SSL 3,ISTP1 
SSL(3,ISTP + 2) 
SSL(3,ISTP + 1} 






SHS(1,1 
SHS \',2 
SHS, 1,3 
SMSi2,1 
SHS{2,2 

sash, 3 

SHS(3,1 
SHS (3 ,3 
SHS(3,2 






3500 CONTINUE 

cSS«Int : S«Sg| ,r£ 5 s i*IS > S I l§ a l!l J !& a I55fS I ?J 1 .5 fS!g ASD *™w nx 

Qonu hh. m ** z mMW/$T * «5g D!?!L^SiNT LC s\ D Afl H i Aiaix onlt on 

COBHENT^ADD IN Jcl^ADS ' SJX 'SJY, SJZ, SJV,SJXY, C JX ,QJY , QJZ, QJT) 
IF (NITF .SO. 1 .AND. IIIPE ,JQ. 1) GO 10 3550 



3550 



QJX 

qjy = o.o 

QJZ =0.0 
CONTINUE 
IF ( IBVESE .NE, 



COHHENT - STO^E:|6rfsE n iF BEVEBSAL°OC 5 OBS LATEB 



3580 



35&0 



C0MH2NT 



CQHKENT 
COHHENT 

3600 

3700 



4000 



COHHENT 



EBXXOL(JTN 
EBYYCLiJTN 
EBZZOL (JTN 

GO TO 3590 

CONTINUE 

ERXX (JTN 
ERYY (JTN 
EHZZ (JTN 

CONTINDE 
FSS 
FSS 
FSS 

ADD IN J._ 

SSL{1,1 
SSL(1,2 
SSL (2,2 
SSL(3,3 

if (itype :ra 

IF (ITYPE . EQ. 4 



EBXX 
EfiYY 
EBZZ 



JTN 

JTN 

JTN 



E8XX0L(JTN 
EBYYOL{JIN 
EBZZCLfJTN 



< (i) = fss (ii + 

(25 = FSS 2) ♦ 
]3) = FSSJ35 + 
OINT restraint: 



= FSS (1 
= FSS J" 

= FSS? 
T RESTRAINTS 
= SSL(1,1 
= SSI 1,2 
= SSL/2, 2 
= SSL 3.3 



EBXX (JTN) 
ERYY (JTN) 
EBZZ(JTNJ 



QJX 

CJY 
QJZ 



+ SXX(JTN) + 
+ SJXY 

+ SYY(JTN) ♦ 

♦ SZZiJTN) + 



. 3) CALL ADDYN (JTN. PSS1 

.„IS«I? ^l Q i it CAL1 ADDrsjjTN'.Fls 

r SSL TO FACILITATE OBTAININGSO 



SJX 

SJY 
SJZ 



OF SSL 

CO 3600 I = 1,IHB 

SSL(2,I) = SSL(2. I + 
DO 3700 I = 1,IHB1 



FBOH 2ND AND 3RD BOK 



1) 



SSL(3,I) = SSL(3,I ♦ 2) 
SSL{2.IHBP1) = O'O 

SSL(3,IHBP1) = 0.0 

SSL(3jlHB) ' = O 
CONTINUE 
DO 4500 11=1,3 

IF(SSL(II,1) . NE. 0.0) GO TO 4500 
2f|C 0^ DiAGOSAL «ATEtx - DISPL ACEHENT ONDEFINED - SET 



COflBENT - DISPLACEMENT EOOAL TO 1.0E40 
§§i(il.»1) =1.0 



4500 

COMMENT 
COHHENT 



4700 
5000 



5100 
5200 



6000 



FSS (II) = 1. 0E40 
CONTINOE 

IF (APBOB .NE. PBINT) GO TO 5000 

P°«S OF STRUCTURE STIFFNESS AND LCAD BATEIX, TO ACTIVATE SET 
DO^4700 II-° L 3 MNS IN EfiCBLEK f,aaBEE CA EE EQ^AL TO PRINT 
CONTINUE 50 ' ' (SSL(II ' J ) .>1.IH8J1) , FSS (II) 
CONTINUE 

J1P1 = J1 ♦ 1 

J1P2 = J1 + 2 
IF (HI .EC. -1) GO TO 5200 
DO 5100 J2=1,IHEP1 

RH(J1,J2) = SSL(1,J2' 

EH J1P1,J2) = SSL 2^J2' 

SM|J1P2,J2) = SSL 3'J2 



CONTINO. 

BO(JI) 
HO (J1P1 
K0(J1P2 

CONTINO 
BETUEN 
END 



= FSS(1 
) = FSS (2 
) = FSS 



05513 
06514 
05515 
06516 
06517 
06518 
06519 
06520 
06521 
06522 
FF 06523 
06524 
06525 
06526*75 
06527 
06528 
06529 
06530 
06531 
06532 
06533 
06534 
06535 
06536 
06537 
06538 
06539 
06540 
06541 
06542 
06543 
06544 
06545 
06546 
06547 
06548 
06549 
06550 
06551 
06552 
06553 
06554 
06555 
06556 
06557 
06558 
06559 
06560 

06561 

06562 

06563 

06564*72 

06565*72 

06566*72 

06567*72 

06568*72 

06569*72 

06570*72 

06571*72 

06572*72 

06573*72 

06574*72 

06575*72 

06576*72 

06577*72 

06578*72 

06579*72 

06580*72 

06581*72 

06582*72 

06583*72 

06584*72 

06585*72 

06586*72 

06587*72 

06588*72 

06589*72 

06590 

06591 



****"u^uii*NETAr«nTnr^ 



2b 



DIHE DO I 25 AA ^'^5 BB ( 3 ' 3 > »CC(3,3) 
DO 25 J = 1*3 

CC(I,J) = CO 
DO 25 K = 1,3 

CONTINui I,J) = AA(I ' K) * EB ' K ' J ' + CC{I,J) 
RETURN 



06594 

06595 
06596 
06597 
06598 
06599 
06600 
06601 
06602 
06603 



288 



END 



06604 




25 



c(i) = 5.o 

DO 25 K = 1,3 

C(I) = AA (I,K)*B(K) 

CONTINUE ' 

BETURN 
END 



C(I) 



06610 
06611 
06612 
06613 
06614 
06615 
06616 



****************** ************^** t 




*********************** 



C03KEHT - THE SDBEO0TINE ITSELF KEEPS TRACK OF THE DEFORP! ATTnN nTSTnov 

JNTSPB * COEVE (OF THE 



SSSSfeSl " BEPiacEs the previous sdbrootines 

COMMENT - EAHLIEH VEBSION FBAH61) 
IHELICIT EEAL*8 (A-H.O-Z) 



COHHON /BLOCK1/ 2(25)," ' 
SXX(25), 
DZZ(25| - 

EHi"Y(2E 

NSYT 

1ST,.' 



COH 



X(25|, 25), 

X 25], NSYY(25[; 

,.~P{25). ISIJfi(25f 

SON /BALA01/ QVV(25!) . 

RW(2S), NSVV(25) 



NSX 
NSY 



CCH30N /8LCCK2/ DXS('25) 
FRF( 25 



DC 2S( 2 5),' 
i (2a) 



PRAG 



: ''1,2S) , 

NSXR"( 25), 



NAL( 25 1 



ELEKN(25) , 
IPIKL 25). 
NSXL( 25), 
NSYE( 25) , 



UB(10, . 

M 25 ii 
SYYf25) , 

RXXJ25J , 

£az2(25) , 
NSZZ(25), 

SV?(25) , 

DYS( 25), 
PEAE( 25) , 

IPI8R( 25) , 



DBT(10) 

QXX(25) 
SZZ (25) 
EYY (25) 
QHJ 25} 
IHJ (25) 



L 



DVV(25) , 

ZLS( 25) , 
Qfl( 25) , 



NSYL( 2 5) , 



NSZBl 



SC51 
NSZL 
NCDS 



QYY(25) 
DXX(25 
RZZ (25 
HHJ(25] 
NSXP(2I 



ERVV(25) , 

DC1S( 25) , 
»H( 25), 



.CCaHOK 
2 NQJ 



. qW, B/ MUM' 

SS?S2i /.IhP./. *NLOPl J ,IFAE,KCFFJ,KOFFQW,KO?FSE 



< 25) , INLCPf 25) , 
( 25), NAB( 25) . 
( 25) . IAXOPS (25) 

ISJ( 20), NQJ< 20,11),N«J( 20,11), 



codaos /SKT1/ 
COMMON /SKT2/ 

HRV (25,10), 
WRTY (25,10i, 
WRTYP{25. lOf 
KOFFJ 



SfiJT(2C,10), KMAXJI(20,10) 

HBX(2 C " 1n ' Bev/ti in> '/„„', 

KEXPf : 
S'BIZ i 



25,105. B£Y(25,10), SRZ(25,10), 
' 25,lM, WSYP<25,1D)', HHTi(2fi.lbf, 
,(25,10), 8BIV(2S;10 ), WBTxJ> (IS, l6f , 



COBBIIII - fOFF-J^O I. EFFECT SETS NO LIMIT ON DEFORMATION 

NC = NSXX(JTS) 
NPTT = NPT(NC) 
NPTTB1 = NPTT-1 
DC 3509 I = 1,KFTTH1 

UE (I) = HEX (JIN, I) 
OET(I) = WETX(JTN.I) 
H (I) = fcBJ JTN) * huji fNC, I) 

3509 CONTINUE ™ KX{1) = ^ (JTN > * 2 K AXJI(NC,I, 
TEMPI = NQJ(NC,2) 
TEMP2 = Nk/J NC.2) 
SLPHAX = TEHP1*Qk 
KJ = DXX(JIN) 

CALL DO C 3400 i =nNPTTB1 J ' K J ' 2 J2 ' SJX ' D£ '°BT, JTN, 1 .SLPfiAX ) 
»RX (JTN^I) = OR (I) 
-,,„. KBIX (JTN,I) = UET (I) 

3400 CONTINUE 

GO TO 3511 



^QilJ<JTN) / TEMP2 / KMJ (JTN) 



3510 CONTINUE 



3511 



IF 



QJX = 0.0 
SJX = 0.0 



( NSYY(JTN) .EQ. 
~""Y(JTN) 



) GO TO 3520 



3519 CONTINUE 



NC = N'SYY(JTN) 
NPTT = NPT(NC) 
NPTTH1 * NPTT-1 
DO 3519 I = 1,NPTTH1 

BE (I) = £EY (JTN, I) 

CRT (I) = KETY(JTN,I 

B (I) = WKJ (JTN) * WWJT 

EHSX I) = QMJ (JTTJ) * 



) * SHJT (NC.I) 
N) * BHAXJT(NC,I) 



TESP1 = 
TEEP2 = 
SLPHAX 



NQJ 
N 



»M(HC,2) 

iWJ{NC,2) 

TEHPl*Qt 



QHJ(JTN) / TEKP2 / »«J(JTN) 



WJ = DYY(JTN) 
CALL CUEVIN ( NPTT, «, feMAX, * J, QJ Y ,SJ Y, OP ,URT , JTN, 2,SLPB AX ) 



********** 
06617*75 
06618 
06619 
06620 
06621 
06622 
06623 
06624 
06625 
06626 
06627 
06628 
06629 
06630 
06631 
06632 
06633 
06634*70 
06635*75 
06636*42 
06637*42 
06638*42 
06639*42 
06640*42 
06641*42 

mn 

06644 

06645 

06646*84 

06647*84 

06648*84 

06649*84 

06650 

06651 

06652 

06653 

06654 

06655 

06656 

06657 

06658 

06659 

06660 

06661 

06662 

06663 

06664 

06665 

06666 

06667 

06668 

06669 

06670 

06671 
06672 
06673 
06674 
06675 
06676 
06677 
06678 
06679 
06680 
06681 
06682 
06683 
06684 
06685 
06686 
06687 
06688 
06689 



289 



3410 
3520 

3521 



DO 3410 I = 1,NPTT!11 

«EY (JTN, I) = OB (I) 

HETY(JTN,IJ = UiiT(I) 

CONTINUE ' M ' 

GO TO 3521 
CONTINUE 

QJY = 0.0 
SJY =0.0 
IF ( NSZZ(JTN) .EQ. ) GO TO 3530 
NC = NSZZ(JTN) 
NPTT = NPT(NC) 
SPTTH1 = NPTT-1 
DO 3529 I = 1,NPTTB1 

Ufi (II = BEZ (JTN, I 
UfiT(I) = &ETZ(JTM. 
B (I) = HMJ (JTN) 
EHAX (I) = QHJ (JIN) • 



«,I 

i) * vs 



3529 CONTINUE 



JT (NC.I) 
EHAXJT (NC.t) 



TEMPI = NQJ(NC,2) 
TEKP2 = KKJ(NC'2} 

^ P = A DZZ(jflif 1 * QflJ(JTN) ' TEHP2 ' BWJ ( JT ») 



3420 
3530 

3531 



CALL DO [J 3420 i 5 P ^,ff|fiAX.WJ,QJZ,SJZ,UB,UBT,JTll,3,SLPflAi ) 

HEZ (JTn'i) = OS (I) 

£TzlvJTN,lj = UET(lj 



HBZ 

CONTINUE 

GO TO 3531 
CONTINUE 

QJZ = 
SJZ = 



0.0 
0-0 



) GO TO 3540 



3539 CONTINUE 



IF { NSW (JIN) .EQ. 

NC = NSVV(JTN) 

NPTT = NPT(NC) 

NPTTM1 = NPTT-1 
DO 3539 I = 1,NPTTH1 

Ufi fl) = WBV (JTN, I) 

U3T{I) = 8ETy JTN, I) 

B (I) = WKJ JTN) * WKJT (NC-I) 

R3AX(I) = QMJ (JTN) * BKAXJT{n6,1) 



TEHP1 = N0J(NC,2) 
TEHP2 = NWJ(NC,2) 
SLPKAX = TEHP1*QKJ(JTN) 



■3-i "Dyv(jiN) " - ~" ' TESP2 ' BKJ<JTN > 

'' I = i 6^|5 AX ' i ' J '2 JV ' SJ V,UE,nET,JTN,4,SLPflAX ) 



30 3430 
HRy 



3430 
3540 

3541 



CCNTINU 

GO 
CCNTINU 



1,NPT1H1 
(JTN, I) = UB (I) 

UBT(I) 



aaiv (jtn, i) 

3541 



IF 



DC 



QJV = 0, 
SJV = 0. 



NSXP (JTN) .EQ. 0) 
NC = NSXP(JTS) 



GO TO 3550 



3549 CONTINUE 



,-tS) 
nptt = npt(nc) 

nptth1 = nptt-1 

549 I = 1,NPTTM1 
UE (I) = WBXP (JTN, I) 
UfiTJI) = WETXP{JTN,I) 
H (I) = SB J (JTN) * iWJT 
BHAX (I) = CMJ (JTN) ■■■ 

TE3P1 = NQJ(NC,2 
T2HP2 = NfcJ NC ' 
SLPMAX = TEHP1 
ISTT = ISTJB (JTN 



) * iWJT (NC.I) 
N) * EHAXJT (NC, I) 



'A 

*QHJ(J 



TN) / TEHP2 / RHJ (JTN) 



CALL CU 
DO 



»5"= DCiMIST"Tf*DXX(JTN) +DC2S (ISTT) *DYY (JTN) 
VIN j SPTT^^&MAX,WJ,QJT,SJT,0E,URT,JTN,5,S1PH 



440 



AX ) 



3440 CONTINUE 



W2X? (JTN, I) = 
HHTXP(JTN,I) = 



UB 
UBT 



3550 
3551 



CONTINU 

IF 



gjX = QJX + QJT * DCIS(ISTT) 
QJY = QJY + QJT * EC2S(ISTT) 
SJX = SJX + SJT * EdSflSTT ** 2 
SJY = SJY + SJT * EC2S(I5TT) ** 2 
SJXY = SJT » DOS (ISTT) * DC2S (ISTT) 
J55 1 



SJXY = 0. 
( NSYP(JTN) .EQ. 0) GO TC 3560 
NC = NSYP(JTN) 
NPTT = NPT(NC) 
NPTTK1 = NPTT-1 
DO 3553 I = 1,SPTTH"I 



UB (I) = WBYP (JTN, I) 
UETJI) = HBTYP(JTN,I) 
3 (I) = SiHJ (JTN) *' 



3559 CONTINU; 



(i) 

BBAX (I) 



(JTN) 
QBJ (JTS) 



8HJT 
* F.HAXJ 



(NC.I) 
T (NC " 



I) 



K :H 



TEMPI = NQJi 
TEHP2 = NHj(NC' fi :) 

ISTT A = ISTJE(JTsf J(JTN) ' TEMP2 7 KKJ < JT1, > 



06690 

06691 

06692 

06693 

06694 

06695 

06696 

06697 

06698 

06699 . 

06700 

06701 

06702 

06703 

06704 

06705 

06706 

06707 

06708 

06709 

06710 

06711 

06712 

06713 

06714 

06715 

06716 

06717 

06718 

06719 

06720 

06721*84 
06722+84 
06723*84 
06724*84 
06725*84 
06726*84 
06727*84 
06728*84 
06729*84 
06730*84 
06731*84 
06732*84 
06733*84 
06734*84 
06735*84 
06736*84 
06737*84 

06738*84 

06739*84 

06740*84 

06741*84 

06742*84 

06743*84 

06744*84 

06745 

06746 

06747 

06748*84 

06749 

06750 

06751 

06752 

06753*84 

06754 

06755 

06756 

06757 

06758 

06759*84 

06760*84 

06761 

06762 

06763*84 

06764 

06765 

06766 

06767 

06768 

06769*84 

06770*84 

06771 

06772*84 

06773 

06774 

06775 

06776*84 

06777 

06778 

06779 

06780 

06781*84 

06782 

06783 

06784 

06785 



290 



CALL 



3450 CONTINUE 



3560 CC 21 UNITE 
BEIUBN 
END 



• HYP (JTN,I) = OE (I) 
KBIYP(JTN,lJ = UEljl) 



X ) 



QJX = QJX - 
3JX ■ QJY + 
SJX = SJX + 
SJY = SJY + 
SJXY = SJXY 



QJT * DC2S(ISTT) 

QJT * ECIS(ISTT) 

SJT * DC2S/IST1 ** 2 

SJT * DCIS(ISTT) ** 2 

- SJT * DCIS(ISTT) * DC2S(ISTT) 



06787*84 

06788*84 

06789 

06790 

06791*84 

06792 

06793 

06794 

06795 

06796 

06797*84 

06798 

06799 



******* ************* 

5UBEOUTINE COBV 

IMPLICIT EE 

COMMENT - ALL THE COH 

DIMENSION (10) 

COMMON /BLKT/ 

2 KESP2, 

3 KEEP5B, 
<i NCD3B, 
5 NCD5D, 
o IABAN, 

7 api. 

COMMON /BLK5/ 3 
COHHON /5KT3/ N 
COMMON /SKT6/ 
COMMON /SKI 14 / 

COMMON /SKT18/ 
COSMOS /SKT19/ 
COMMON /SKT22/ 



ccaaENT 

COMMENT 
COMMENT 
COMMENT 



IN THIS STJB 
AXIS HAS A 
IS TAK 
SUBBOU 
NPTM1 
B = C. 
BK = 
( INDEX 
1000 K = 
UB (K) 



CABE 
WITH 



IF 
DO 



IN ( N 

AL*8 ( 

MENTS 

,BHAX( 

TOL, 
KEEP3A 
KEEP5C 
NCD4A, 
NCD6, 
IPOBB, 
MP2, 
FSUB.N 
COUNT, 
NI 
IEV (2 
IKVBS 
NCHECK 
JCEGCN 
TIME, 
BOUTIN 
NEGAII 
EN TC 
TINE 
= 1JPT 


-0 

.HE. 1 

1.NPT 

= UB1( 



******** 
PT,W,EHA 
A-H.C-Z) 
UNDEB SU 
10) ,UB(1 

ELEBN1, 
,KEEF3E, 
,KEEP5D, 

NCD4B, 

NCD7, 

SB, 

ISTI. 
ITF.Nl.N 

NI1ERF 
TEBM(50) 
1.2.10). 



SUBBOUTINE *********************** 
X,U,B,BK,Dfi,UBT,JTN,JCXrZP,SLPMAX ) 

BBOUTINE INELST APPLY HEBE 



0) ,UBT(10) 

NJ5T, KE£P3C,NCD3C, 
SIP? a '£IPi! B ' KBE P i 'C,KEEP5A, 

KEEir6, KEEP7, NCD2, NCD3A. 

NCD4C, NCD5A,' NCD5B, NCD5cJ 

IP8, IP9, IP10, ITYPE' 

NJT, NSl! NLT,' M, ' 

LIT, ITYPEL,IDJ, NSTL 



, INDEX 
ITAPE, 



FOHOID(50,6) , 
N3 ' 



(25,6) , JCUBEV (25,6) 

JT, IBDYN, IBSTEP(71) 

E, II SHOULD BE NOTED THAT THE HESISTANCE 

VE aULTIPLIEB AS INPUT. HENCE PBOPEE 

ACCOUNT FOB THIS . COEPAEE 5 CGNTEAST 

MASING ( STBESS-STEAIN ROUTINE) 



GO TO 1100 



1000 CONTINUE 
1 100 CGNTINOE 

DC 2000 



COSKEUT 



»" K = 1.NPTH1 

STIFF = fiMAX (K) / W(K) 



5.0D-10) ) GO TO 1500 



THE ABOVE s MINUS + SIGN ISMII! IN SIGN CONVENTION CF PEOGBAB 
!. I ) GC TO 1450 



1450 



IF ( 
IF 
IF { 

30 T 

:ont 

IF ( INDEX 

CM K .EC 
50 TO 1800 



NCHECK . NE. 



i [ g •■■,' 



GC TO 
30 TO 



[ GC 

:hgon. 



) GO TO 1450 



= 



nn*i a in; 
:ECK . NE. 1 ) GO TO 1550 
•NE. 1 ) GO TO 1550 
GCN (JTN,JCXYZP1 . NE- 1 



JCBGCN (JTN,JCXYZP 

JCUBEV (JTN,JCXYZP 
GO TO 1800 
CONTINUE 

T- , UST(K) = UBJK 
H P D U '? Q r 1 1 SC TO 1800 
££ i^ilZfr T > JCBGON(JIN,JCXYZP) 
1500 CONTINUE 

IF ( . (JT. UH (K) ) GO TO 1600 

„„,?=- KMAX(K) 

IF NCHECK .NE. 

IF { K 

IF ( JCfiGCN (JTN,JCXYZP) . NE. 1 1 

JCUBEV (JTN,JCXYZP) = 1 
GO TO 1800 
CONTINUE 

usij;k) = a + h(k) 

IF ( INDiX .2Q, 1 ) GO 10 1800 
IF ] K .EC. 1 ) JCH 
GO TO 180C 

Z = EMAX(K) 
IF ( NCHECK .NE. 
IF } K .NE 

IF ( JCBGCN (JTN,JCXYZP) . NE. -1 ) 

JCUBEV (JTN,JCXYZP) = 1 
GO TO 1800 ' 

CONTINUE 

UBI (K) = U - H (K) 
IF { IS DEI .EQ. 1 ) Vc TO 1800 
CON-flHU* ] JcfeG0N ( JTH »JCXYZP) = +1 

fi = E + Z 
CONTINUE 
IF I ITYPE ,L£. 2 ) GC TO 2050 

GO TO^OO ' EQ - 1 " ANC - NITZEF '**' 2 > 
CONTINUE 



GC TO 1550 



1550 
160C 

1650 

1800 
2000 

2050 



■"*£» • / *JW J.KJ I owu 

1 ) JCHGON(JTN,JCXYZP) = -1 



ti) 

E. 1 ) GO TO 1650 

E. 1 5 GO TO 1650 

K,JCXYZP) .NE. -1 



GO TO 1650 



GO TC 2100 



********** 
06800 
06801 
06802 
06803 
06804*79 
06805*61 
06806*61 
06807*61 
06808*61 
06809*61 
06810*61 
06811 
06812 
06813 
06814 
06815 
06816 
06817*84 
06818 
06819 
06820 
06821 
06822 
06823 
06824 
06825 
06826 
06827 
06828 

06829 
06830 

06831 

06832 

06833 

06834 

06835*90 

06836 

06837 

06838 

06839 

06840 

06841 

06842 

06843 

06844 

06845 

06846 

06847 

06848 

06849 

06850 

06851 

06852 

06853 

06854 

06855 

06856 

06857 

06858 

06859 

06860 

06861 

06862 

06863 

06864 

06865 

06866 

06867 

06868 

06869 

06870 

06871 

06872 

06873 

06874 

06875 

06876 



291 



2 .AND. NITEEF .EQ. 2 ) GO TO 2100 



2100 PV1o' e = 

2100 CONTINUE 

IF ( gC a l Ey (JTN,JCXIZP) .EQ. ) GO TO 2200 

2200 C0NTIN^ fiEV{JIS ' JCXI2r > " ° 

BETUBN ( NCHKK - £ Q- 1 ) Ifi?RSE = ItVESE + JCtJEEV (JTH, JCXYZP) 
END 



8»?2 

06879 
06830 
06881 
06882 
06883 
06884 
06885 
06886 




ELK... 

IPI2JL , 
NSXL( 2 5)', 



I 22)', 



PH, 

L25J, IPINR( 25) , NC51( 25 

"in (251 

;ZB] 25) 
'( 22) ,' 

J 22 it 



DC1SJ 25) , 
WH( 25), 



NSYEJ 25 
F( 22 
QX 

DZ 

02r22j. 
B32S( 22), 1 
SEET{6,6)_ 

ELEMHT, 



NSYLf 2 5)',' NSZL* 25 
NSZBJ 25) . 



AE 
EEX ( 

sgz( 

V2( 

TTS{ 



f: 



22. . 
22) , 
22), 



NCDSJ 25 
SX 

QZ 

EE_ ,. 
U1( 22 
B2j 22 
AG? 22 



INLOPf 25) , 
NAB( 25), 
IAXOPS { 25) 



( 22 , SY( 22), 

( 22j, DXj 22[; 

U 2%, EBz'f 22), 



*****sSBES0TINE*F^82nBr* B r + I6 S P£f 0D "" ********************************* 

&S8iii : r fCIJ|J EgK'ttlfaHa' 1 *** siLe of sraaEIEIC STIF ™ ESS «»« Sifir 72 

06 889*74 

06890 

06891*72 

06892 

06893*42 

06894*42 

06895*42 

06896*42 

06897*42 

06898*42 

06899 

06900 

06901 

06902 

06903 

06904**5 

06905 

06906*79 

06907*61 

06908*61 

06909*61 

06910*61 

0691 1*61 

06912*61 

06913 

06914 

06915 

06916 

06917 

06918*72 

06919*72 



VI ( 22)', 
05(3,3, 



22), 



_J ( . 
PBAG(25), 
| IOPOPf 25), 
? NAL{ 25), 

NSXB( 25/ . 

. coaaoN /dLockV 

2 SZ( 22) , 

3 DY 22$, 

1 Sc2( 22) , 

5 «H 22), 

6 BfilSf 22), 

coanoN /Blociv 

COMMON /BLK 1/ 1 uv< 

2 "5**. KEEP3A,KEEP3B KEeMa,KEEP4B;kEEP4£ KEEP5A 

3 KEEP5E,KEEP5C,KEEP5d;KEEE6, KEEP7, NCD2. NCD3A 

5 IZMl: K?' h h SK- !ir ; IpT A - ?l? !*• Ill' 

§ IA3AN' IFOBB, HE, NJt! »--' «- ' i TIPE ' 

7 „ SP1. 3P2- istt, ltt! 

coaaos /blk2> xl,xb\xi,x2, ' 

ccaaos /3LK5/- nf5ob;nitf,ni,h2 

COMMON / 21 / SI, fl£, J1 

IAXOET = IAXOPS(ISTT) 
COMMENT - I If STATION H |U« - bl IS ELEMEKT NOB - J1 15 EQUATION N0« 

J1 =3*1-2 



TOL 



NJST, KEEP3C, NCD3C, 



NST, NIT, fl, 
IIYPEL.IDJ, NSTL 
H,TH,HSQ,HCU,X21,I1,I2,NQ 



IF 
IF 
DO 
DO 



fl .NJ 
1600 



1) GO TO 28 
GC TO 2100 



00 



1600 
2100 



2300 



2400 
COSilENT 

CALL 

2500 
C0H3ENI 



. EQ. - 
HE. 1) 

J J = 1, 3" 
1600 KK = 1, 3 

SEBS (JJ,KK) =0.0 
CONTINUE 
CONTINUE 

¥o iko LT JJ H I 1) 1 J° T0 2 " 00 

DC 2300 KK = 1,6 

_SEETUJ,KK) = 0.0 



GO TO 250 

IP1 = I + 1 

CALL ELEflST TO OBTAIN 6X6 
ELEBST ( IP1,JIITf ) 



ELEMENT STIFFNESS SATEIX 



2600 

COMMENT 



2650 



CONTINUE 

DO R 2600 fi£ Jj a = B 1 °3 KEflBER S; "IFNESS MATEIX SEM 

DO 2600 KK = l' 3 

CO K TI^f (ji ' KK) ■ U**W 3;^K + 3 3, 
ADD IN SPEING STIFFNESSES 

SEM(3,3) = SEH(3,3) + SZ (I) 

f I iifflh 1 .iS^af.rf?!o I 5fc- afc TC2650 



3) 



IF 
IF 



COMMENT 
2700 



2 800 



2M 1,1 
38(2,2) 

>800 



SEM(1,1> = SEE (1,11" + ' SX (I) 
- SEH(2'2) + SY(lf 



3600 
3700 



SE 

GC TO 28. . 

HEflSEH SPHINGS 

SXT = SX(I) 
SYI = SY(I) 
CALL SANGLE (SA , SXT, SIT) 
SEMM, 1) = SEB(I^I) \ 
SEM 1,2) = SEM 1,2) < 
SEM (2, 1) = SEM 2, 1) < 
SEM 2,2 = SEE 2; 2 4 
EEHl.1) = EBX(I) 
FEB (2) = EEY(I) 

DO 360^¥= = a zW 

DO 37eo Etl ^^ ) 1 ;, SEH(2 ' K * 1 » 
SEB(3,K- 



IN STSUC1UEE DIEECIIONS 



SA?2,1 
SA(2,2j 



SEM(2,6 
SSM (3,6 
SEH(3,5 



SEB(3,K + 
= 0.0 
= 0.0 
= 0.0 



2) 



06920 

06921 

06922 

06923 

06924 

06925 

06926 

06927 

06928 

06929 

06930 

06931 

06932 

06933 

06934 

06935 

06936 

06937 

06938 

06939 

06940 

06941 

06942 

06943 

06944 

06945 

06946 

06947 

06948 

06949 

06950 

06951 

06952 

06953 

06954 

06955 

06956 

06957 

06958 

06959 

06960 

06961 

06962 

06963 

6 964 

06965 

06966 

06967 



292 



JlP2 = Jl + \ 06968*72 

IF (ML .EC. -1) GO TO 5200 06969*72 

DO 5100 J2=1,6 06970*72 



EH(Jl,jJh = SEK(1,J21 06971*73 

EH J 1P1 ,'j2) = SEH|i'j2 06972*72 

C1 n,. RajJlP2,J2) = SEH 3 J2 06973*72 

5100 CONTINUE^ ' l '^' 06974*72 

5200 KO(JI) = FEH(1) 06975*72 

20/J1P1) = FEM(2) 06976*72 

,„„„ B0JJ1P2) = FEB (3) 06977*72 

6000 CONTINUE * ' 06978*72 

fiETOEN 06979*72 

END 06980 

06981 

*"*"*S0BBoSlHrE2HST*ri*IITJ*r SUBE0UTIHE ********************************* 

COBBENT - ITERATION NITF= 1) H N F0BHiD - ( CNLI ON FIRST 06985 

gg^I^? : E»L%m Hi 1 f °W& '# ^ B rail*ii*K.i H loi 0,M 81111 

06990 

D(6,6), TH(6,S) 06992 

f/M 22?}* AEf 221. <;y/ oo, „, ,„ 96??3*14 

l lft'3f!- HKIfe- IflJJI: ItiW. 




isfiK. lv < ;. > • Ufa): aw:-* 



2), 06998 



AS I 22) 06999**5 



6 DaTSf 2l) , BM2S( 22) TT' 

coaao« /hochS/ seet 6,6 ' 

CCMHOS /3LK1/ TCL. ELHBNT NJST fFtov vrmt* 07000 

! ilrilfffP fe* P f If |jl! 

6 IA3AN' IFOJxfi, SB. NJI wfl* ntt ' £ TYPE » 07005*61 

7 HP1, HP2, ISTT LIT' ttyps-t ?n?* 5*m, 07006*61 
COMMON /htk/5/ yt yd »i »4t ' *>**» l-LIPaL, IDJ , N5TL 07007*61 



07010 



COMHON /3KT8/ SSiR.Uf V2TK21), «2TT(21) 07011 

COMMON '/SS1\% / IRV(2i;i, , FCBOLD f50 6) niVA 

2 IRVRS2. ITAPF wo (30»o) » Q701 3 

COMHON /SKT23/ PDELTA ' «*«# N3 07014 

COHHON /SKT35/ THESTP 07015 

£ a t1 t5Ih'2iyiI&/ HCB * Mraw |o 1**3 

IF ( ITYPE .IB. 2 | 1e"1p = ANCNF 07020*16 

CoSSIS? " f&fc = I P-DEi.TAlfFECTS A ARE E CONSIDERED MM} 

C0BHM.T " LOCAL^^ = P-DELTA EPFEC1S AfiE NOT CONSIDERED 07023 

IF (PDELTA. EQ : PDKO -OH. PDELTA. EQ. PDN) LOCAL = 07025 

IF (ELEKNT . EQ. SHEAR) GO TO ?oon 07026 

COMMENT - COYOTE ELEMENT DEFcIb ATIONS 2 ° ?MU** 9 

DDX = 0X(I) - DX(If1l 07028 

MX = DI if - DI IBll 07029 

DZ1 = DZ 121) U1{± "'> 07030 

DZ2 = DZ if ° 7031 

IF ( LOCAL .KE. 1 GC TO ^n 07032 

COME,! - CO.POT. "FO.^8,1 I| S |g |JW jg.IlCMB g?SJ3 

BHt : S J« ' mil 

TAD1 = 1HETA - DZ 1 07037 

mm - ifi$]h\lfk KJP^mhflF'HfiHT""""'" Hill 

DO 100 K = 1*3 07042 

100 BT(J,K) = 0.0 07043 

Bih'ij = -i.o 07oau 

BT 4,1 = 1.0 07045 

BT(2'2) = -1 1 / H 07046 

BT \3',2) = - 5 / 07047 

BT 5,2) = 1.0 / H 07048 

BT 6,2) = -0.5 07049 

BT(2^3) = 10/ B 07050 

BtUU) = 0.5 / 07051 

BI5 J = -10 / fl 07052 

BTi6^3 * 15 / 07053 

GO TO 400 07054 

300 CONTINJE 07055 

COSIB1 =DCOS (DZ1) 0^056 

COSI =DC0s}d22J 07057 



293 



CJKflEST 



SIHIH1 = DSIN(DZ1) 
Sj.NI =DSINfDZ2) 
COSCCS = COSI + COSIH1 
SINSIN = SIKI + SIKIH1 
8 = CDX + H*M.O - 0.5*COSCOS) 
S = BDY - 0.5*H*SINSIN ' 

HPS = a * 8 
HPD = DSQBT(aPB*HP8 
DELTA = HPD - H 

THETA =DATAN (S/EPB) 
TAU1 = THETA - DZ1 
TAU2 = DZ2 - THE1A 
COEPUTE PCfi CONVENIENCE 



S*S) 



HPES1 
HPES2 = 
HPEC1 = 
HPiC2 = 
SC 1 
SC2 

SSI = 
SS2 
HPDE1I = 



HPE*SINIB1 

HPB*SINI 

HPB*C0SIB1 

HPE*COSI 

s*cosiai 

S+COSI 
S*SINIB1 
S*SINI 
1.0/HPD 



COMHENT 
COMBENT 



FORK 

hath: 



100 



500 



CCKHENT 

COBSEKT 

700 C 



ST 3,2 
BT (4,2 
BT [5,2 
BT (6,2 

BT 2,3 
BT 3,3 
BT (4,3 

BT|6,J 
CONTINUE 
IP (IFAE .2 
DC 500 J = 
DO 500 K = 



HPDE2I = HFDE1I+HPDE1I 

H02 = 0.5*H 

THE TEANSPCSE OF THE EIEiJENT DEFOBBATION-DISPLACEBENT 

= -fl£E*HPEE1I 
= -S*HPD£1I 
= HC2*HED£1I* {HPBS1 
= - BT(l,r 
' - Bfj2.1l 
= H02*HPDE1I* (HPBS2 
= S+HPDE2I 
= -HPE*HPE£2I 

1.0 -HC2*HPDE2I* (HPSC1 + SS1) 



BT 

BT 
BT 
BT 
BT 
BT 
3T 
3T 



1,1: 

3 ' 1 
*#i 

5,1 

1*2} 

2,2 



- SC1) 
SC2) 



= -BT(1,2) 
= -BTJ2,2[ 

= -H02*HPDE2I*(HPEC2 + 
= BT{4,2) 
= BTJ5.2J 

= HC2*HFD1 
= BT{1,2) 
= ET(2,'2 

= 1.0 - Bl(6,2) 



SS2) 



DE2I*(HPEC1 ♦ SS1) 



1.3 



30 TC 700 



AIL 



710 



D(J,K) = DS(J„K,I) 

TT = risiiV 

B21 = BMlS(I) 
BH2 = BH2S(I) 

GO TO 800 

CALL FAEEEV TO FIND INTEBNA 
iLEHENT FCECE-DEFOEiUTICN a 
FA.&BEV (DELTA, TA01, 
THESIP .Efi. AMES ) GO 
ITYPE .20. 3 .OH. ITYP 
IBVSSE .SE. ) GO TO 
, SI IF . GT. 1 ■ 
CONTINUE 

IF ( LOCAL .HE. 
= J B 



ATEIX C D S IN EL£HE!,X TT,BB1,BB2 A 

10*710 If D ' TT ' BK1 ' BH2 » 
E .EQ. 4 ) GO TO 800 

) GO"TC"800 



750 



COMMENT 



doo 

COH3ENT 

C 

CO H.1 EST 



V1TT 

U2TT 

V2TT 

U1TT 

WITT 

Si2 TT 

GO TO 800 

CONTINUE 

SINT 

COST 

VT 

STORE FOE 

U2TT 

V2TT 

U1IT 

V1TT 

WITT 

W2TT 

CONTINUE 

FOEH FIHST 



) GO TO 
K2 - 3B1 



750 
) / B 



= -VITT(I) 
= -U2XT(l( 
= -BH1 + 5. 



BH2 



V1TT(I) * H 
V1TT(I) * H 



/ ( H t DELTA 
§ * 3 I / ( H 

BH2 - Sal ) / 
BY FCBBLE 
= TT * COST + 
= TT * SINT - 
= - U2TT (I) 
= - V2TT M 
= - Bfl1+0.5*( 
Bfl2+0.5*( 



+ DELTA ) 

+ DELTA ) 



( H 

VT 
VT 



07059 

07060 

07061 

07062 

07063 

07064 

07065 

07066 

07067 

07068 

07069 

07070 

07071 

07072 

07073 

07074 

07075 

07076 

07077 

07078 

07079 

07080 

07081 

07082 

07083 

07084 

07085 

07086 

07087 

07088 

07089 

07090 

07091 

07092 

07093 

07094 

07095 

07096 

07097 

07098 

07099 

071O0 

07101 

07102 

07103 

07104 

07105 

07106 



im 



* SINT 

* COST 



-UITT(I) *SINIB1+V1TT(I)*C 
-01TT(I)*SINI +V1TI(I)*C0SI" 



►COSIS1 



85 

COMMENT 

C 

CONSENT 



COBKENT - C 



. PAET OF TBIPIE p 
ALL HATHPY (BT , 6,3 , D ,3 ,T 

- FOaa THE ELE8ENT DEFOSBATio 
DO 850 a = 1,3 
DO 850 J = 1,6 

B(K,J) = BI(J.K) 
-COMPLETE l&E TBIPLE PECDOCT 
ALi - T „ TmT aATSEY (TH,6.3,B,6,S 

- INITIAL SIBBSS HAIEIX IS NO 
IF { LOCAL .EQ. ) GO TC 

OHPUTE FCfi CONVENIENCE 

= HFDE2l*HPDE1I 
= S*S 
= HPE*HPH 
= TT*HPDE3I 



JTE FCfi 
HPDE3I 
SE2 
HPEE2 
TTM 



ECDUCT 

8) 

N-DISPLACEBENT BATBIX 



EET) 

9999 E " DELT4 EFFECTS IGNOEED 



07109 
07110 
07111 
ND 07112 
07113 
07114 
07115 
07116 
07117 
07118 
07119 
07120 
07121 
07122 
07123 
07124 
07125 
07126 
07127 
07128 
07129 
07130 
07131 
07132 
07133 
07134 
07135 
07136 
*H07137 
•H07138 
07139 
07140 
07141 
07142 
07143 
07144 
07145 
07146 
07147 
07148 
07149 
07150 
07151 
07152 
07153 
07154 



294 



COKBEKT 



TTHHC2 = TTH*H02 
HPDE* = HPD+HPD 

COHPOTE THE POBTIOS OF THE INITIAL STBESS KATBIX DDE TC TH 




THi3,5i 
TH/3,6 
TH l 4,4 
TB|4,_ 
TH i 4,6 
TH(5,5 
T8|5,6 
TH(6,6 



= TTH*SE2 
= -TTa*S*BFE 

= -TTHHC2 *S*(SS1 + HPBC1) 
= -TM (1,1) ' 

= -TH(1,2 

= -TTMH02 *S*(SS2 ♦ HPBC2) 
= TTM*HPBE2 ' 

||H*H02»aPB*(SS1 + HPEC1) 

= -TH(2,2) 

■ TTHH02 *HPfi*(SS2 + HPRC2) 
= ITMH02 *(H02*(SS1 + HPEC1)**2 
HPDE2* SSI + HPBCIj) 



= -TH 1,3 
= -TH(2,3) 
= TTHH02 > 
= TH(1 r 1 
- 181,2 
= -THi 1,6 
= THi 2,2 
= -THi2,6 
= ITHH02 



H02*(SS1 ♦ HPBC1)*(SS2 ♦ HPBC2) 



COHMBNT 



998 



COHHEiiT 



*(H02*(SS2 ♦ HPBC2)**2 + 
N1 , HPDE2* {SS2 ♦ HPBC2J) 

DO D 998 T K I L ^ fl f NT STIFFNESS HATBIX 

HI =~Nl'+ 1 

DO 998 J = HI, 6 

CONTlioT (S ' j; = S2ET ^.J) ♦ , H(I ,J, 

VT = (BB2 - BH1)/HFD 

VTH = VT*HPBE3I 

VTMHC2 = VTH*H02 

HPES = HPBE2 - SE2 
C03PDTE THE POBTION OF THE INITIAL STBESS EATBII DOE TO SH 



Tfl 

Ta 

TH 

T3 
TH 



1,1, 
1,3] 

i,b 



-VIH*HPB*S*2.0' 
VTH*BPBS 
VTHB02*(HPsS*CCSIH1 

3 » 1 r 



TM 
TK 

H*arfis* 



TH (2,2 
TH(2,3 
TH(2,4 
TH(2.5 

.5 



= -la(], T) 

= -TM(l'2) 

= _yTfla02*(HPBS*COSI 

THH02*{ 



+ S*HPfi*SINIH1*2.0) 



■ -TH 
= V 



+ S*HPR*SINI 



TH(1,5) 
■ (2^21 



*2.0) 
HPBS*SINIH1 + S*HPK*CCSIH1*2.0) 



-TH 



= VTMUC2*(-HPES*SINI + S*HPH*cr<!T 
= "VTHH02* HPDE2*{HPB*SINIH1 
*CCSIH1 ♦ H V *HPB*S*<SINI21**2 



VTHH02*|HPDE2*^HPB*SINIflr- a s*COSIHTT--V 

- COSIH1**2 



"SalaS? «=IH filar —*——»«*»*«•»»;« - 

Ta 3,51 = -Tab, '3 

T2(3,t>) = -VTMHG2*H02*(HPBS*(SINIH1*CCIST + 



*2.Q) 



CCSIH1*SI 



= TH(1,1 

= THi'1,2 



CONSENT 



999 

' 2000 

COHHENI 



Td (4,4 
TH(4,5 
TM (4,6 
TH(5,5 
18(5,6 
TH(6,6 
H*HPES*SINI 
HI = 

00^999 T K J LI j H g KT STIFFNESS HATEIX 

N1 = N1'+ 1 
DO 999 J = HI, 6 

SEET IK, J) = 5EET(K,J) 

SiiET (J,KJ = SEET(K,JJ 
CONTINUE l ' ' 

GO TO 9999 
CONTINUE 
COHPUI'E EIEHENT DEFCEHAIICNS 

DDX = DX ■" 

DD 

DD 
IF (LOCA 
IP 



= -Tfli 1,6) 
= TH 2,2) 
= -TH(2,6) 

■ -VT8H02»(HPDI2*iHPE*SIHI 
♦CCSI + B *HPB*S*(SINI **2 



+ TH(K,J) 



S*COSI ) + 
- COSI **2 



: EIEHENT DEFCEHAIICNS 
| = DX(I) - DX(IHI) 
I = D*M - DY(IK1) 
Z = D^(I). ~ DZJIH1) 
AL . NE. 0) GO TO 2300 



COfiKENT " C0H ^ L 1|p£F G 5™CNS BASED ON SHALL DISPLACEHENTS 



COHHENI 

COH.1ENT 



.100 



TBETA 

DELA 

PSI1 

PSI2 

DELS 

DELH 



DDY/TB 
= DDX 

= DZ(IHI) - THETA 
= DZ(I) - 1HETA 
= H*JPSI1 + PSI2) 

gf | H |ri|ll!A H ?^M? E ^I5i| " DISP " CE ™ ««H BASED 

DO 2100 K = 1*3 

B(K,J) = C.O 

B 1,1 = -1.0 

B 1,4 - 1.0 

B (2,3) = -1.0 

3(2,6) = 1.0 

8(3,2) = 1.0 

B 3,3 = H 

B(3,5 = -1.0 



BOST07157 
07158 
07159 
07160 
07161 
07162 
07163 
07164 
07165 
07166 
07167 
07168 
07169 
07170 
07171 
07172 
07173 
07174 
07175 
07176 
07177 
07178 
07179 
07180 
07181 
07182 
07183 
07184 
07185 
07186 
07187 
07188 
07189 
07190 
07191 
EAB 07192 
07193 
07194 
07195 
07196 
07197 
07198 
07199 
07200 
07201 
07202 

mi 

)) 07205 
07206 
07207 
NI) 07208 
07209 
07210 
07211 
07212 
07213 
07214 
07215 
)) 07216 
07217 
07218 
07219 
07220 
07221 
07222 
07223 
07224 
07225*17 
07226**9 
07227**9 
07228**9 
07229**9 
07230**9 
07231*19 
07232**9 
07233**9 
07234**9 
07235**9 
07236*17 
07237**9 
07238**9 
07239**9 
07240**9 
07241**9 
07242**9 
07243*43 
07244**9 
07245**9 
07246**9 
07247**9 
07248*18 
07249**9 
07250*18 



295 



B(3.o) = B 
,.„,.,, GO TO 2460' 

23U0 continue 

C0H3ENT - COMPUTE FCH CONVENIENCE 
THDX = TH + DDX 
THDXI = 1.0/THDX 
THETA = DA1AN(DDY*1HDXI) 
PSI1 = D2 IB1) - IHETA 
PSI2 = DZJI) - THETA 

COS2 = DCCS(PSI2) 

SIN1 = DSIH(PSH) 

SIN2 = DSIN(PSI2) 

COSCCS = COS1 + C0S2 

SINS IN = SIN1 + SIN2 



SINT = DSIN(THETA) 
(THETA) 



sinc: 
:os{: 

2.0*1 



COSI = DCOi 

SIN2T = 2.0*SINT*CCST 

COST2 = COST*COST 

D£LA = THDX/COST - H*COSCOS 

DELS = H*SINSIN 

CCflSESI - EOSH EL2SENT°DlF0flHAIICN DISPLACBHENT aATBIX 



8(1,1) = 

B. 1 .2 1 = 

BilJI 

B 1 4 

B(1,5. 



•COSI - DELS*SIN2T*liJDXI/2.0 
■SJNT *DELS*COST2*THDXI 

-El 



H _ 

0.0 

i'i\ = 0.0 

2,3} = -1.0 

'2,4j = 0.0 

■ 0.0 



m 



B(1,1) 

♦SIN2 



2400 



2500 



B: 2,6 
3(3, 1 
3(3,2 
B(3,3 
B 3,4 
3(3,5 
B(3,6 

CONTINUE 

IF UFAE .20. 

DO 2500 J = 1,3 

DO 2500 K=1,3 



= -BJ2.3) 

« -fi*SIN2T*COSCOS*THDXI/2.0 
= H*COST2*CGSCOS*THDXI 



= "B (3,1) 
= H+COS2 



1) 30 TO 2700 



5i J ' K iL = DS(J,K,I) 
TT = TTS (I) 
3H = 3HS(I 



C 

CO MM 
27 



sh = sasti) 

SO TO 2800 ' 

n \mih'*h. 3 oi°ib mhfi- « so to 28o ° 

") 6( 



•SX> 1) SO TO 2800 




2710 CONTINUE 

IF (LOCAL .HE. 0)__GO TO 2750 

V1TI 

Mil (I) = -Ba + fl*sa 

U2TT 
V2TT 
H2IT 
GO TO 280 
27^0 CONTINUE 

DELAE2 = 
DELSE2 = 
-OHSEHT - ST03S FOH USE 
U1TT (I 
V1TT (I 

a itt (i 

2 TT*(H* 

U2TT (I 
V2TT(I 
W2TT ?I 
2 TT*(H* 

CONTINUE 

ENT - FOHfl FISSl PAET OF TBIP1E PBCDOCT 

DO 2850 J = 1,6 
M BT(J,K) = BIS., J) 

"^ W^II* l IM&h b mn? P-OELTA 



280 
CO MM 



H*SH 



DELA/2.0 
DELS/2.0 
- BY FCEflLD 
= -TT*COST 
I = -TX*SINT 
I ■ -BB + SH*(H*COS1 
3IN1 - DELSD2) 
I = -U1TT(I) 
= -V 1TT(1 
1 = BM + SH*(H*C0S2 
3IN2 -DELSD2) 



SH*SINT 
SH*COST 



DELAD2) + 



+ DELAD2) 



285 
CO MM 
CO MM 
COM 



. . IF (LOCAL . EQ. CJ*~3o"t6"999 5' 
ESI - C03PUTE FCR CONVENIENCE 

COS21 = 2.0*COST2 - 1.0 
J.HDX12 = THDXI*THDXI 
C0ST3 = COST*COS'I2 
C0ST4 = COST2*COST2 
SIN2T2 = SIN2T*SIN2T 
HT = a*TT 
HI I = BT*TEDXI 



EFFECTS AHE IGNOEED 



072S2*ll 

07253*19 

07254*19 

07255*19 

07256*19 

07257*19 

07258*19 

07259*19 

07260*19 

07261*19 

07262*19 

07263*19 

07264*19 

07265*19 

07266*19 

07267*19 

07268*19 

07269*19 

07270*24 

07271*19 

07272*=19 

07273*19 

07274*43 

07275*19 

07276*19 

07277*19 

07278*19 

07279*19 

07280*19 

07281*19 

07282*19 

07283*19 

07284*19 

07285*19 

07286*25 

07287*25 

07288*19 

07289*19 

07290*19 

07291*19 

07292*19 

07293**9 

07294**9 

07295**9 

07296**9 

07297**9 

07298**9 

07299**9 

07300**9 

07301**9 

07302**9 

07303**9 

07304**9 

07305**9 

07306**9 

07307**9 

07308**9 

07309*19 

07310**9 

07311**9 

07312**9 

07313**9 

07314**9 

07315**9 

07316*19 

07317*19 

07318*19 

07319*19 

07320*19 

07321*19 

07322*19 

07323*19 

07324*19 

07325*19 

07326*19 

07327*19 

07328*19 

07329**9 

07330**9 

07331**9 

07332**9 

07333**9 

07334**9 

07335**9 

07336**9 

07337*19 

07338*19 

07339*19 

07340*43 

07341*19 

07342*19 

07343*19 

07344*19 

07345*19 

07346*19 



296 



COMMENT 
COHHSSX 

2 

2 



- «SME T !oI H |o J ^!I^I. fHlBIl STIJ?FH£SS HAlfiIX IB THE SHEA* 
ISH'^ - -HII*SIK2T*COS1/2.0 



ST2 + fl+SIB2T2*CCSCOS%.5 1) 

-XI + THDXI2*(DEIS*COS2T 



TM { 1 , 5J 

Tah;6 

TMJ2.2 

H*CQST 
M (2,3 

TM (2,4 



• -Ta 

= -l'J_. 

= -HTI*Slti2T*CGS2/2. 
*COSCoin SI3 * THDXI + THEXI2 *< D2 "*SIN2T*C0ST2 + 
= iiTI*C0SI2*COS1 



can,i) 



TM 
TH 
TH 
TH 
TM 
TH 
TH 
TH 
Tfl 
TH 
TM 



2,6 
3 * 3 , 

3#f.l 

3,0 

4,4 

4,6 

I»f: 

5,o 



COMMENT 



2S98 

COMMENT 
COMMENT 



TM(6,6 
N1 = 



= -TH(1,2) 

= -TMJ2,2)_ 

= HTI*COST 

= HT*C0S1 

= -TM(1,3) 

= -TM(l.B) 
= TM(2,2) 



2*C0S2 



-T 

ET 



S&l- 



- ^ D 299 d ' T K | L ^ B P T STIFFNESS MATRIX 

si = iii +1 

DO 2998 J =S1,6 

CONTINgF (K ' J) = SEET < K ' J > + TM(K,J) 

: §§SSE , !oS H fo p $$gSL°lHlH SII?FHESS HATEI * in TflE she A2 

ns = u*sh 

881 = HS*TBDXI 

'2*C0SC0S + 

coscos + 

If M'fJ = HSI + sfH2T*SIN2/2.0 

Iliif^CGSCOS) 2 * ( " DEXS * CCST4 + H*C0ST2* 

TM(2,3) = -HSI*C0S12*SIN1 




TM (2,41 
TK{2;5 
TM(2,6 
TM (3,3 
TM (3,4) 
TM 3,5] 



= -TM(1,2) 
= -THJ2C2) 

= -HSi*COS 



. 2SI2*SIN2 
-HS*SIH1 
-TM(1,3) 



Tfl (1,1) 
TMh,2[ 

1M (2.2)° 
-TM(2,6) 

-HS*SIN2 



TM(3,6 

TM (4,4) 

TH(4,5) 

TM}4,6) 

TM(5,5 

TM{5,6 

TM (6, fa 

N1 = 

CGHilENI - ADD ON TO ELEMENT STIFFNESS MATRIX 
DO 2999 K = 1,6 

N1 = N1+1 
DO 2999 J = N1,6 

SEET(K,J) = SEET(K,J 

co N ti S nPe t1j ' k5 = SEET < K <^ 

CONTINUE 

I? ( ????£ .SE, 3 ) GO TO 1000 



2999 
y999 



IH(K,J) 



1000 
COSHENT 
CGKMENI 



1100 CON 
1200 



• EQ. ) GG TC 1400 



IF ] IFAE 
CONTINUE 

IN° fi HEMlNI F0LI,CBING FCK END ELEHEN,r S ONLY FOB IATEE DSE 
IF J I .MS. 2 I GO TO 1200 



DO 
DO 



1300 CON 
1400 CON 

RET 
END 



..J. 2 ) 
00 K = 1,3 
1100 J = 1*1 
juE SESE (8,3) = SEEI (K,J) 

DO 1300 J = 1,6 

SSEE (K,J) = SEET (K.J) 

IINUE 
UHN 



07347*19 

07348*19 

07349*19 

07350*19 

07351*43 

07352*20 

07353*43 

07354*19 

07355*19 

07356*43 

07357*19 

07358*19 

07359*19 

07360*19 

07361*19 

07362*43 

07363*19 

07364*43 

07365*43 

07366*19 

07367*19 

07368*19 

07369*43 

07370*19 

07371*43 

07372*19 

07373*19 

07374*19 

07375*19 

07376*19 

07377*19 

07378*19 

07379*19 

07380*19 

07381*19 

07382*19 

07383*19 

07384*19 

07385*19 

07386*19 

07387*19 

07388*19 

07389*19 

07390*19 

07391*24 

07392*19 

07393*19 

07394*19 

07395*19 
07396*19 
07397*19 
07398*19 
07399*19 
07400*19 
07401*19 
07402*19 
07403*19 
07404*19 
07405*19 
07406*19 
07407*19 
07408*19 

07409*19 
07410*19 

0741 1*19 

07412*19 

07413*19 

07414*23 

07415*19 

07416 

07417 

07418 

07419 

07420 

07421 

07422 

07423 

07424 

07425 

07426 

07427 

07428 

07429 

07430 

07431 

07432 

07433 

07434 



297 



SS£° T ?gE INCBEHENTAL FOBCE-LEFOEMATIOB HATBIX FOB AS Pfl*p5? 
FOS LINEAE SIBESS-STBAIN CHB?ES (INLOPT = 0) THE FnriATTnSI N n P 
*MH 21 ABE USED FOB BCJUIkIaI SIbIsI-STSAIS CORVES F 

(-i.Ni.OPT = 1) A NOMEBICAL INTEGRATION TS nowv t-UKIfJib 
BIIH SOME LIMITATIONS GN THE SIG-EP CUB7I iIpUT CAPABIi IT v 

DIMENSION Dj6,I) l ' ' 
DIMENSION TTMP(2), BMTHP(2), AETBP(2). 
nEfl|2 B8TEH 2 AETEH 2 ,' 
EPSCOM 10), SIGCOBMO) 
SIGHIS(2J, STFHIS(i) ' 

DYS( 25), 
PBAF.( 25f, 



C 

c 
c 
c 
c 

COaHEST 
c 



DIMENSION 
DIMENSION „ 
COMMON /BL0CK2/ 

2 DC2S{ 25) , 

3 PEAG{25), 
« IOPOP( 25) - 
5 HAi ( " 



AEYTHP(2) , 
AS ITEM (2) ' 



EITEM 



81- 



HSXE( 25 



_JBN(25f, 
IPIH1.L25;, 



PEF 
ELE 



ZLS{ 25) 
Q"{ 25), 



DClSf 
*M( 2 



5> 2 f> 



USIL 

NSYE 



25 
25 



JT2J50) 
F( 22), 
QX< 22) , 
DZ 22K 



I PINE ( 25) 
NSYL( 2 5) 
NSZF.} 25) 



iH 



NC51 

NSZL 
SCD5 



COMMON /BL&CK7/ 

2 SZ{ 22), 

3 DY( 22j; 

1 SQ2{ 22}, 

5 tffj 22). 

6 SHTSl 22) , 
COMMON /BLOCKS/ 

2 YCL( 10), 

3 DEPSL(10. 11) ,ia»i 
COMMON /BLGC12/ SM(20,'10 

2 11(20,10) / Hsi{28.1v 

COMMON /3LOC13/ NPT3( 5s) 



BMis ( 25) , 

BCL(ir 

DYCL 
,ISS 



t (ii[, 



HUB (50). 
AE( 22), 
QY 221 , 

EBXf 22), 
5QZ 22i' 
V2( 22 
TTS ( 2_ 
DBCL(10 




IN10P( 25) , 
NAE ( 25) , 
, IAXOPS( 25) 
IT (50), ' 

IMC (50) 
5i( 22) , 
DX( 225, 
EBZ( 22), 
71 < 22), 
DS(3,3, 22), 



SIG Hl?»]i) , epsl(i6 



: nsitmi) , heptJid' ' l 

COMMON /BL0C15/ EPST 2 1 . SIGTf 
COfidON £|LK1/ / TOL, ' ELEMNlfNJST 



DCLHO 
. .) , E?SL( iu, 
NSSLjIO), NSSB(l5) 
EH(20,ld), 31(20, tO) i DI(20.10). 
N tI19»Ao, NCDA(20), IBE<*T(20,16) 
ISS( 08), NSIG(08jl) ,NEPS 08;il/, 



07436 

07437 

07438 

07439 

07440 

07441 

07442 

07443 

07444 

07445 

07446 

07447 

07448 

07449 

07450 

07451*42 

07452*42 

07453*42 

07454*42 

07455*42 

07456*42 

07457 

07458 

07459 

07460 

07461 

07462 

07463 

07464**5 

07465 



DDCL(IO). U/46S 

11) ,DSIGL(10, 11), 07466 

07467 



SIGTS (1 1) 



COMMON 
COMMON 



: ■■■HAi V: ! iI:SS!5«]l ) J!Iili:Iltise'KiE«; 

KE2P5B, KEEP5C,KEEP5d'kEEE6- SEEP7 NCnP Nrnft ' 
NCD3B, NCD4A,'nCD4B,'nCD4C NCD5A,' NCD5B, "- iht 

IP8, IP9, ' 

NJT, NStJ 

LTT, ITYPEL 
H.TH.HS 



NCD5D, NCD6, NCD7, 
IA3AN, IFOfift, SB. 
SP1, MP2, ISTX, 
/BLK2/ XL,Xfi x X1 t X2, 



/SU7/ IHLCpf.IFAE'KCFFJ.KOFF&OoF: 



2 CO««ON/ITC/ §f|1 fi EKg2 5 Efi1 fi |H2.0TI,CH,BII,HH (20) 
COMMON /SKT10/ ' NDlf (20-10> HvrTnT t ->n\ 

aSSSSS 'AIV4 aa Simil'M). S H i P i fl T ?x[o 2 8 0) ,03, 



, NCD5C, 
IP10, ITIPE, 
NLT, M, 
IDJ, NSTL 
.HC0,X2I,I1,I2,NQ 



,MJ(20),MNITF, 



coaaENi 

COMMENT 
COMMENT 



8) , BE 

U 8 )! 3I 
TO 1500 



ETA (8)', 
IG0L1(8) ' 



MATBL 



'HI 



AND NOBBEE 



1500 

COMMENT 
COMMENT 



COMMON /SKT3 1/ ALPHA (8 
SLOPHD 
IF (I . GT. 2) GO ., 
- SKIP FOB ALL BUT FIBST ELEMENT 

: Sg H 58B o N 'F H L E «BE c L aiGID EL2a ^ TS 

UR a - IPINL(ISTT) /10 

NLE = NL2 + NE 
NE = - IPISB (ISTT) /10 
B|_ » - IPINB ISTT - 10+NE 
Una = dP2 - NE 
NEE = NBE - NE 
CONTINUE 

IF (INLOPT . EQ. 1) GO TC 2100 
" COMPUTE THE USX AND BENDING MOMENTS AND TNTR 
i MATEIX FOB ELEMENT HITH LINEAE 

= F(i)^ ta 

= D 2,2) 

= 0.0 

= 0.0 

= 0.0 

= 0.0 

= 0.0 

= 0.0 



2? L ^ P (§}' E?STHD(8), 



COMMENT 



2100 



(1.1 

iiji 
2,3 
3,1 

BM2 = 

TT 
IF (I .GT. NLE ".AND. I ",LT. NEE) GO "?n 41fin 
MULTIPLY HWE^BIIO FCE BIGlT ELEME^ 4 ^ 




A/TH 



BM2 = BM2*iO.'0 
TT = 11*10.0 



COMMENT - SKIP FOB 



0U.2 

0(3,3 

GO TO 4100 
CONTINUE 
IF jl .GT 



1, 1 

2,2 
i,3 



*10.0 
♦10.0 
♦ 10.0 



• 2) 

ALL 



GO TO 2500 
BUI FIBST ELEMENT 



07468 

07469 

07470 

07471 

07472 

07473*79 

07474*61 

07475*61 

07476*61 

07477*61 

07478*61 

07479*61 

07480 

07481 

07462*88 
07483*88 
07484 
07485 
07486 
07487 
07488 
07489 
07490 
07491 
OF LINEAE ELEMENTS07492 
07493 
07494 
07495 
07496 
07497 
07498 
07499 
07500 
07501 
07502 
07503 
EHENTAL FOBCE 07504 
STBESS-STEAIN CUBVE07505 
07506 
07507 
07508 
07509 
07510 
07511 
07512 
07513 
07514 
07515 
07516 
07517 
07518 
07519 
07520 
07521 
07522 
07523 
07524 
07525 
07526 
07527 
07528 
07529 



298 



COHHENT 
COMMENT 
COHHENT 



I 9§SI°ll T iI C ?lS H JHCRXIK A.I HEBBEES 



AKD EIFFEBENCE IH THESE PBOPEfiTIES BETWEEN FBOfl 



DO 



COMMENT 
COMAE NT 

COMMENT 
COHHENT 
COMMENT 
COMMENT 



FfiOH JOINT 

TO JOINTS 

KALI = NAI(ISTT) 
NASI = NABJISTT) 
NCDAX = NCIA(NALT) 
2200 J = 1,NCI>AI 

BCL(J) = Bl(NALT,J) 
OS?i <J> = (Sl(NABT'j) 
DCL(J) = DI(HALT,jf ' 
DDci(j) = JDKNaStIJ) 
*CL(J = Yf[NALT,jf ' 
DICLJJ) = (Vl(NABT;j) 

nssijj} = nssJsaiiJjJ 
&sslt = nssl(j) ' 



IF 



BCL(J))/a 
ECI(J))/K 
YCL(J))/H 



IF ( 



NDIV(NALT,J) .NE.OT 
Sf§£J J > = HSS(KABT,JJ 
NSSEI = NSSB(J) ' 

NSi 



GC TO 2200 



DC 



HPTST = NPTS(NSSIT) 

2180 K = 1.NPTST 

|fSL(J,Kj = NSIG(NSSLT,K)*SH (NALT.J) 
" gSIG(NSSHT,K)_*SHiiJABT,J) 



2180 

2200 

2500 
COMMENT 
COHHENT 



SIGB 

EPSL(J,K) ='NEPs7NSSLT7ib"*EM'[NiLT Jl 
E?SB = Nbs(NSSal,K)iEH(NA£T'j) ' J) 
DSIGL J,K) = (SIGl(J,K) - SIGB5/H 

CONTI^! SL < J ' Ki = 1""lIj;kJ - EPSbJ^H 

CONTINUE 

CONTINUE 

(IE 



- (IE 



IF 
IF 
IF 
IF 



COKHEMI 



COKHENT - ZEEO 



= 1) FOB 
= 1 FOB 

IB = 

IE = 
I .LE. NLB 
I -LE. NLE 
I .GE. NBB 
I -GE. NEE 

ZHOL = I 

ZHCL = ZMOL 



EIGID ELEHENT 
LINEAR ELEHENT 



IB 
IE 
IB 
IE 
2 
<p 



1 
1 

1 

1 

0.5 



BENDING HOBENTS, AND STIFFNESS TEBMS 



COMMENT 
COHHENT 
COMMENT 



COMMENT - 



COHHENT - 
COHHENI - 
COHHENI - 
COMMENT - 



2560 ccn: 
COHBENT - 
COHHENT - 
COHHENT - 
COHHENT - 



COMMENT - 
COHHENT - 



TO KEEP TBACK 

AND THEIB COMOLATIVE 



COHPUTE DEFOEMAXIONS IN ELEHENT 

EP = 0ELTA/TH 

CUB1 = TA01/H 

COE2 = TAU2/H 

ELEHENT THROST, 

BH1 = 0. 

BH2 = 0.0 

T1 = 0.0 

T2 = 0.0 

Ell = 0.0 

EI2 = 0.0 

AE1 = 0.0 

AE2 = 0.0 

AEY1 = 0.0 

AE3T2 =0.0 

D(2,3) = 0.0 

D(J,2) = 0.0 
INITIALISE THE PABAHE1EB THAT IS OSED 
OF THE (PEESCRIEED) SUBDIVIDED PIECES * < 

P0SIT icdh5 ^g LICA " 2 lei inIlastic CASE ohly" 

DO 4000 J = 1, NCDAT 

COMPUTE SECTION PB0PE2TIES AT MID-ELEHENT 

B = BcL(J) + ZHUL+DBCL(J) 

D? = ilCL(J) + ZMUL*DDCL(J) 

NPIST = NPTS(NSSLT) 
COHPUTE STEESS-STBAIN CDBVE AT 
NCN-LINEAB ELASTIC CASE. 

DO 2560 K = 1,NPTSH1 

SIGCCHfK) = SIG.1AX(NSSLT,K) * SMfNALT Jl 

iMBt EPSCCH W " epsieiIbssli.'kJ * eh {halt J jj 

COKpSheNT SIG^EPI CORviiP 3 COaPUT ^°* S *°* ™2 
NOW ALSO COMPOTE THE MAXIMUH 
VIBGIN SIG-EPS CUEVE FOE USE 

= SMfNALT, J) 

= EMJNALl'j 

= NSiG <NSSLT,2) * 

= NEPS (NSSLT.2) * 

= SIGMA / PSLON 



HID- ELEHENT ONLY FOB THE 



£P CDBVE AT 
CE TO JOINT. 



SHSCL 
EHSCL 
SIGMA 
PSION 
SLPdAX 



INDIVIDOAL 

SLOPE AT THE OEIGIN OF THE 
IN STBAIN BEVEBSAL CHECK CASE 

SHSCL 
EHSCL 



07530 
AND07531 
07532 
07533 
07534 
07535 
07536 
07537 
07538 
07539 
07540 
07541 
07542 
07543 
07544 
07545 
07546 
07547 
07548 
07549 
07550 
07551 
07552 
07553 
07554 
07555 
07556 
07557 
07558 
07559 
07560 
07561 
07562 
07563 
07564 
07565 
07566 
07567 
07568 
0756 9 
07570 
07571 
07572 
07573 
07574 
07575 
07576 
07577 

07578 
07579 
07580 
07581 
07582 
07583 
07584 
07585 
07586 
07587 
07588 
07589 
07590 
07591 
07592 
07593 
07594 
07595 
07596 
07597 
07598 

07599 

07600 

07601 

07602 

07603 

07604 

07605 

07606 

07607 

07608 

07609 

07610 

07611 

07612 

07613 

07614 

07615 

07616 

07617 

07618 

07619 

07620 

07621 

07622 

07623 
,07624 
B07625 



299 



COMMENT - (FOE MILD STEEL ) 



pUHi : &&£i aIIiSB8 !S E IS6 S SHI^i HE il c St LUES fiAVE 3EES 



GO 
2590 CO 



2600 



SMALL 
EPHD 
SLHD 
SULT 
ALP 
BET 
TO 3910 
NIINUE 
DO 2600 
EPS 
SI. 
(ISST 
2610 K '= 



SKLSLP 

EPSTHD 

SLOPHD 

SIGOLT 

ALPHA 

BETA 



K = 1,NPTST 



NSSLT) 
NSSLT) 
NSSLT) 
NSSLT) 
NSSLT) 
NSSLT) 



SECUB. 

SMSCL / EMSCL 

EMSCL 

SMSCL / EHSCL 

SKSCL 



IF 
DO 



pflf!) Z IflH'i'iJ + ZMUI+DEPSL(J,K) 
K = 1 _ ndtci't 



1, NPTS 



2610 
2650 

2675 



SIGT(K) = SIGTS(K) 



GO 



DO 



= EPSTS(I) 
-, = SIGIS 1) 
2, NPTST ' 

♦ NPTST - 1 



2700 
COHaEKT 
COMMENT 

coaaEUT 



COMMENT 



CO MM EST - 

COMMENT ■ 

CCBflBfll - 

CAi 



COMMENT 



COMMENT 
COMiiE.NI 
COMMENT 
CA 
2 
COMMENT 



- 2*(K - 1) 

= EPSTS(K) 

■ -EPSTS(K) 

= SIGlSfK) 

, = -3IGTS (K) 

2* (NPTST) - l' 



CONTINUE 

ISSTT = 

NPT = NPTST 
TO 2700 

EPST(SPTST) 

SIGT (NPTST) 
2675 K 

KS = 

Ki = 

EPST 

EPST 

SIGT I 

SIGT 

NPT 

ISSTT 
CONTINUE 

!3rayilBJHiL>IB* , IUBawWfiBl«HIii«OT« 

NPP = 1 
IP (I2ECT (NALT.Jl .Eg. 1) NPP = 10 

rU^f.'J^J^l CA1L PIPE (B,DP,J,IP,NPP) 

FAEJR (T,BM,EA,EI,AEY,ISSTT,NPT,Y,B,DP,EP,CUB1,IB,IE, 
ACCUMULATE VAlSIsWill 1 ! lclif|£gF' S > 

£11 = Ell + EI 
AEY1 = AEY1 ♦ AEY 
AE1 = AE1 +• EA 
T1 = T1 + T 
C^L FAEJa TO COMPUTE AXIAL THRUST. BENDING MOMENT ANn 

""" ( S T H!SA E |pI^iI E NffIc6^G, r ' B ' DP ' EP ' CnH2 ' Ia ' IE ' 
• ACCUMULATE VALUES FOH ALL EECtInGLES 

EI 2 = EI 2 + EI 
AEY2 = AEY2 + AEY 
AE2 = AE2 + EA 
T2 = T2 + T 
CONTINUE 
TO 4000 
NTINUE 

- INELA3TIC E CASE F0LL0KIHG ADDITIONAL TERMS USED IN THE 
DO 3 915 L 
TTEM 
BMTEM 
AETEM 
AEYTE.1 
EITES 
XT UP 
BKTMP 
AETME 
AEYTBP 

sniff ^ » !i|,ftS2 i g^,vmaBiBiToP»i a B'uaai u , 

DO 3950 IJ = 1.NJ ' 

+ 1 

-EC. 
PIECE 



LI, 



3900 

GO 

3910 CO 
COMMENT 
COMMENT 




ICOMU = ICUMU 
„„„„ , IF i IfiECl (NALT,J) 

COMMENT - SUBDIVIDE THE J TH 
AIJ = IJ 
IE ( IJ . N 
ANJ = NJ 
DDP = DP / ANJ 
YC1 = Y + DP 
DP = DDP 



1 ) GO TO 3920 

AND SUPPLY fl,DP,Y FOE EACH SUB-PIECE 



1 ) GC TO 3918 



* 0. 5 - DDP * 0.5 



07626 

07627 

07628 

07629 

07630 

07631 

07632 

07633 

07634 

07635 

07636 

07637 

07638 

07639 

07640 

07641 

07642 

07643 

07644 

07645 

07646 

07647 

07648 

07649 

07650 

07651 

07652 

07653 

07654 

07655 

07656 

07657 

07658 

07659 

07660 

07661 

07662 

07663 

07664 

07665 

07666 

07667 

07668 

07669 

07670 

07671 

07672 

07673*32 

8?fJ3* 49 

07676 

07677 

07678 

07679 

C7680 

07581 

07682 

07683 

07684*32 

07685*49 

07686 

07687 

07688 

07689 

07690 

07691 

07692 

07693 

07694 

07695 

07696 

07697 

07698 

07699 

07700 

07701 

07702 

07703 

07704 

07705 

07706 

07707 

07708 

07709 

07710 

07711 

07712 

07713 

07714 

07715 

07716 

07717 

07718 

07719 

07720 

07721 



300 



3918 Y = YC1 
GO TO 3 
3920 CALL 
3930 CONTINU 
COMMENT - IF 
IF 
C 

COMMENT - IF 
COMMENT - II 
C 

CALL 
2 
3 

GC 
CON 



9 3o< AIJ 



3935 

c 

COMMENT - SUB 
COMMENT - STH 
COMMENT - OF 
C 

CALL 
2 
3938 CON 
DO 



1-0 ) * DP 

PIPE ( B, DP, Y, IJ, NJ ) 

ALPHA=BETA=0, GO TO BASING SOB 
( ALPHA (NSSLT) +BETA(NSSLT) . LT 

ALPHA*0, BETA=0 Ofi ALPBASBET 
,LD GEOiiTU MODEL, 

DEGSOii (SIGHIS,STFHIS,Y,EP 
SIGCOB.EPSCOK,NPTS 
TO 3938 SMALL, EPHD.SIHD, SO 

TIN0E 

ROUTINE MASING EVALUATES THE H 
ESS AND STIFFNESS, FCB TBE SOB 
BOTH TBE HINGES 152, ACCCBDING 

MASING (SIGHIS,SIFHIS,Y,EP 

SIGCOa,EESCOB,NPTS 



BOUTIHE 

. 1.0D-10 ) GC TO 3935 

A#0 , GO TO DEGRADATION COM 

,CaB1,C0B2,IE,IE, 
M1,ICOHO,I,SL?KAX, 
LT, ALP, BET ) 



3940 CONTINO 
3950 CONTINO 

DO 



39b0 CGSTINUE 



TINOE 
3940 L = 

TTMP 
BMTBE 

AETME 

AEYTMP 

EITME 

E 

E 

BDP = 

3960 L = 
TTEM 
BMTEM 
AETEB 
AEYTEH 
EITEM 



TTMP 

BMTHP 

AETMP 



AEYTMPiL 
= EITMP (L 



TTEM (L) 
BMTEM (L 
AETEM L 
AEYTEM (L 
EIIEM IL] 



SIGH 
SIGH 

STFH 
STFH 
STFH 



ISTOBY DEPENDENT 
-PIECE AT THE LOCATION 
TO BASING PATH 

,C0B1,CUR2,IH.IE, 
M1 F IC&MU,I,SLPflAiC ) 



* Y 

* I 

* Y * Y 




TTMP 

BKTM 
AETM 
AEYT 

EITH 




4 000 
COMMENT 



COBHENT 



4100 

COMMENT 
COMMENT 
CGiijENT 
COMMENT 
C Oil ME NT 
COMMENT 
COMMENT 



4120 
4150 

4160 
420U 

4 26 
4300 



T1 = 11 

BH1 = BM1 

AE1 = AE1 

AEY1 = AEI 

EI1 = EI1 

T2 = 12 

BK2 = BK2 

AE2 = AE2 

AEY2 = AEi; 

EI2 = EI2 
CONTINUE 



ITEE 
SBTEK 
AETEM 
AEYTEM ( 
EITEM |' . 
ITEM 2 
BMTEM (2 
AETEB (2 
AEYTEH (2 



+ EI1EB (2) 



COHPUTE^AVEBAGE^HfiDST AND AXIAL STIFFNESS FOB ELEHENT 

AE(I)'= 0.5* (AE1 + AE2) 
'"UTE INCREBENTAL FOHCE DEFORMATION BATBIX FOE 
5U* 1) = AE(I)/1H 
Di2, 21 = EIT/fi 



COM? 



ELEMENT 



I 



T/E 

EI2/H 

- AEY1/TH 
D(1, 2) 

- AEY2/TH 
D(1, 3) 



DM, 

D{3, 

CONTINUE 
- STOfiE T1 OF THE FIRST NCNLINEAB ELEMENT AND T2 OF THE ijw 

• NONLINEAR ELEMENT , FOB USE LATER IN SUBBOUTINE PBINT9 . 

" ? H SSLS§I !*STEfiIsis CF MONITOR MEEBERS ABE BECORDED ' 
" i ir , H0H EV£E FOR LINEAB MEMBERS AND MEMBERS WITH PIN END(S) 



DO THIS ONLY FOE THE FINAL 
IF ( NITM(JJ) .HE, BNIIB 
IF ( INLCPT -EQ- 1 



lh 



IF ( I .NE 

TTSLEF 
GO TO 4300 
CONTINUE 
IF ( I .NE, 

TTSEGT 
GO TO 4300 
CONTINUE 
IF ( IPINL(ISTT) 



GO 



GO TO 
4120 



SOLUTION OF THE HEMBEB 

2 ) GO TO 4300 

4150 



BP1 ) 



GO TO 4300 



CF ( 

[F I 



2 4. 



NLE + 
= II 



I . NE 

TTSLEF 
GO TO 4300 
CONTINUE 
IF { I . NE. 

TTSLEF 
GO TO 4300 
CONTINUE 
IF ( IPINE(ISTT) 
IF ( I . KE. - 

TTSEGT 
30 TO 430C 
CONTINUE 
IF ( I .NE. 

TTSHGT 
CONTINUE 



GO 



NE. 
10 



4200 



GC TO 4 160 



1 ) GC TO 4200 



MP1 ) 

TT 



NEE - 

= T2 



. NE. 1 ) GC TO 4260 
GC TO 4300 



1 ) GC TO 4300 



Q7722 

07723 

07724 

07725 

07726 

07727 

07728 

07729 

07730 

07731 

07732 

07733 

07734 

07735 

07736 

07737 

07738 

07739 

07740 

07741 

07742 

07743 

07744 

07745 

07746 

07747 

07748 

07749 

07750 

07751 

07752 

07753 

07754 

07755 

07756 

07757 

07758 

07759 

07760 

07761 

07762 

07763 

07764 

07765 

07766 

07767 

07768 

07769 

mi 

07772 
07773 
07774 
07775 
07776 
07777 
07778 
07779 
C7780 
07781 
07782 
07783 
07734 
07785 
07786 
07787 
07788 
07789 
07790 
07791 
07792 
07793 
07794 
07795 
07796 
07797 
07798 
07799 
07800 

07801 

07802 

07803 

07804 

07805 

07806 

07807 

07808 

07809 

07810 

07811 

07812 

07813 

07814 

07815 

07816 

07817 



301 



BET DBS 
END 



mu 



******************** 

SUBROUTINE PIPE 
CCBHENT - SUBROUTINE 
COaaENT - THIS BALLED 
COBflSHX - THE DEPTH A 
CGHMEfiT - TSO EQUAL fi 
IMPLICIT £EAL*8 
DOUBLE PEECISIO 
IE (IP . SE 
2A = 
I = DP 
YC = Y 
DTE = 
ZIP = 
ZIP = 
TE = 
DP = fi 
B = 2. 
Y = YC 
RETURN 
END 



************** suBBOUTIHE ** 

(B,DP,Y,IP,NPP) 
PIPE IS CALLED SPP TlriES BY 

PIPE PIECES- EACH TIHE SUBfi 
ND IBS WIDTH OF A BECTANGLE 
ADIAL SEGHENTS OF THE PIPE P 

(A-H,0-Z) 
N -DABCOS.DSIH.DCCS 
1) GO TO 10 

5* (E - DP) 



10 



DABCCS {-1.0D+00)/NPP 

ZIP - 0.5 
DTE*ZIP 

A*DSIN(TE) *DIE 
*T/DSIN(TE) 
♦ BA*DCOS(TE) 



******************************* 

SUBBOUTINE FAEREY FOB 07821 
OUTINE PIPE FURNISHES 07822 
HBICH IS EQUIVALENT TO 07823 
IECE 07824 

07825 
07826 
07827 
07828 
07829 
07830 
07831 
07832 
07833 
07834 
07835 
07836 
07837 
07838 
07839 



com. 1 ; 

COM3 
COHH 
COBfl 
CCHM 
CO Bit 



COBH 

cosh 



***************** 

SUBBOUTINE FAEJ 

EST - SUBBOUTINE 
EST - SD3-RECTANG 
EST - C0EVE OVER 
_NT - STRESS- SIR 
iKT - AXIAL STIFF 
ENT - STIFFNESS A 
I2ELICIT REAL*8 
DIMENSION DA (22 
COSiiOS /BLOC15/ 
COflflON /BLK7/ I 
DATA S 
EN1 - COMPUTE SIR 
ENT - RECTANGLE 

YB = Y 



*********** 

B (T.BH.EA, 
SH, GA.EP 
FAEJR SUBDI 
LES EACH OF 
IT, FOR THE 
AIN CURVE I 
NESS EA, 3E 
EY 

(A-fi.O-Z) 
),DIj22) ,YY 

EPST(21) , 
NL0P1,IFAE, 
HEAR /5HSHE 
AIN AND Y D 



*** SUBBOUTINE ***************** 

V IDES THE INPUT RECTANGLES INTO 
$?££? S AS 4 LINEAB STBESS-STBA 
NUaERICAL INTEGRATION OF THE 
FIND AXIAL THRUST T, BENDING B 
NDING STIFFNESS EI, AND AXIAL BE 



(22) ,EPCJ22) 
AB/ 



SiGT(2T[,' E?STS(11). 
FQ«,KOFFSE 



SIGTS (11) 



KOFFJ,KOFi 

AB/ 

ISTANCES FOB TOP AND BCTTOfl OF INPUT 



- 0.5*DP 



COKSEHI - 



100 
COM SENT 



200 
300 

C03HENT 



400 

410 

500 

COaBENT 

CGHHENT 

COBilENT 

coaasiJT 



YT 

EPB 
EPT 
B = 
IF (EPB 
REVERSE 
ET 
EPB 
EPT 
YTT 
YT 
IB 
R 
CONTINUE 
FIND FIB 
DO 200 K 
IF (SPB 

NN1 
GO TO 30 
CONTINUE 
NN1 
CONTINUE 
NNP 
IF (NNP 

FIND FI 
DO 400 K 
IF (EPT 

NH2 
GC TO 50 
CONTINUE 
NN2 
CONTINUE 
COMPUTE 

NN3 

NPTT POI 

NPT 

SYKHET.HI 

IF 



= YB + DP 

= EP - YB*COE 

= EP - YT*CUR 
1.0 
.IE. EPT) GO TO 100 
FOR POSITIVE CURVATURE 
- EPB 

- EPT 

= ET 

= YT 

= YB 
- YTT 

1.0 

S = P °NPT ° N SIHESS " SIKAIN CURVE ON OS BELOH 

.GE.'EPST (K)) GC TO 200 

— K — l 


= NPT 

= NN1 + 1 
. GT. NPT) GO TO 410 
EST POINT ABOVE RECTANGLE 

= NNP, NPT 
. GT. EPST (K) ) GC TO 4C0 

~ K 


= NPT + 1 



**************** 
R,IE, 07840*38 
07841*49 
07842 
IN 07843 
07844 
CHENT H, 07845 
NDING 07846 
07847 
07848 
07849 
07850 
07851 
07852*32 
07853 
07854 
07855 



:o«a est 



ZERO THR 
T = 

Ba 

EA 
AEY 
EI 
IF (HII3 
CALCUL&T 



DA 



n 



DI (1 



NUKBEB OF SUBBECTANGLES 

= NN2 - NN1 
NTS OSED TO ENTER STRESS STRAIN CURVE 

9*1 Cjj! fiV I "SE CNLY POSITIVE BRANCH 
4|SST1 .EQ. 1) NPTT = (NPT + 1)/2 

Ust, Bunding mobest and stiffness tehbs 

= o.o 
= o.o 

= 0.0 

= o.o 

. NE. 1) GO TC 1200 

E PROPERTIES FOR liHCLE BECTANGLE 



E*DP**3/12. 



07856 
07857 
07858 
07859 
07860 
07861 
07862 
07863 
07864 
07865 
07866 
07867 
07868 
07869 
RECTANGLE 07870 
07871 
07872 
07873 
07874 
07875 
07876 
07877 
07878 
07879 
07880 
07881 
07882 
07883 
07884 
C7885 
07886 
07887 
07888 
07889 
07890 
07891 
07892 
07893 
07894 
07895 
07896 
07897 
07898 
07899 
07900 
0790 1 
07902 
07903 



302 



5*{EPB + EPT) 



COMMENT 
1200 



COMMENT - 



COMMENT - 



EPCM) = o. 

GO TO 4000 

CALCULATE PROPERTIES FCB FIBST RECTANGLE 

dmi) = = r b*Sd SI(KNP) " " B >/ cu * 
ifjll : yb ♦ o. B 5*E52 /ia - 

HfeOJ = (EPB + EPST(NNP))*0.5 
YIT = YB + DD*B **«••» 

CALCULATE PfiOPESIIES FCB LAST SOBEECTAHGLE 

gA D ^!r ( i p i*BD EPST(sK2 - 1))/cds 

DI(NN3) = E*ED**3/12. 

YIJNN31 = YT - 0.5*DD*B 
EPC(NN3) = (EPT + EPST(NN2 - 111 *0 5 
(NN3 .EQ. 2) (Jo TO 4000 * 1))*0.5 

NN4 = NN3 - 1 
K = NN1 

D^IoQ^I l B 2 P NM IES F ° E EEBAISIHG SQB2ECTANGLES 
K = K ♦ \ 
2?.=r E *(??ST{K + 1) - EPST(K))/CUB 



IF 



A (N) = 

ni : 

?C(K) = 



3C00 
40uQ 
COMMEHT - 



COMMENY - 
COMMENT 

COMMENT 
COM2 EST 
COMMENT 

CAJ 



= B*ED 

B*DD**3 /12. 
, = YTT + 0. 5*ED*fi 
: (N) = Q.5*(EPST(K + 1) ♦ 
= YTT + DD*R 



EPST(K)) 



DA 
DI 
YY 

EPC 

YTT 
COKTINOE 
COJJTIStJB 
DO FOB EACH SUBBECTANGLE 

DO 5000 S = 1,NN3 

EPT ■ EPCjfN) 

ELEMENT**"* 1 ° S T ° EKT1B CDH?E BITB FOfi HIGID 0B "MEAS 
If. (I* -EC- 1 .OS. IE .Eg. 1) EPT = 0.0 

-AC^PU C T ^ I^VD A^ugo^T G flI E B„ / I A S? P f E 5 F ""SS-STR1I. CURVE 

AND STRESS AT CENTSBOID OF SUBR2CTANGLE SIGMA 

E = -II < SIGTS ' EP3TS rEfIr NPIT,ISSTT,SIG,S2,KCFFS£) 
COMMENT - E = 10*1 FOB BIGID ELEMENT 
IF (IB. EC 1) E = 10. *E 
IF (IB ,Bq, *\ .08. IE 

DT = SIG*EA(N) 

DAE = E*DA(N) 

EA = EA + EAE 

EI = EI + E*(DI(N) + DA(N) *YY(N}**2) 



.EQ. 1) SIG = SIG + E*EPC(N) 



5000 
COMMENT 



9000 



BET 

END 



ASY = AEY + DAE*YY (N) 

1 = I + DT 

SM = BM + EI(N)*E*CUR - DT*XY(N) 
CONTINUE * ' 

IF (ELEMNT .HE. SHEAR) GO TC 9000 
LINEAR STRESS-STRAIN CURVE IS ASSUMED FCB SHEAR 

GA = G*B*DP*SHCOEF 

SH = GA*EPS 
CONTINUE 
URN 



07904 

07905 

07906 

07907 

07908 

07909 

07910 

07911 

07912 

07913 

07914 

07915 

07916 

07917 

07918 

07919 

07920 

07921 

07922 

07923 

07924 

07925 

07926 

07927 

07928 

07929 

07930 

07931 

07932 

07933 

07934 

07935 

07936 

07937 

07938 

07939 

07940 

07941 

07942 

07943 

07944 

07945 

07946 

07947 

07948 

07949 

07950 

07951 

07952 

07953 

07954 

07955 

07956*32 

07957*32 

07958*51 

07959*32 

07960*39 

07961 

07962 



************** ******************** SUBROUTINE *********************** 
SUBROUTINE CUEVE IQQ, H«, SJ, NPT, ISYM, QJ, S2, KOFFC) 

- SU3BOJTINE CURVE INTE2PCLATES ALONG A ST3ESS-STB AIN CURVE 
TO FIND TEE STRESS gj CGRRESPCNDI NG TO THE STRAIN HJ AND 
l'B| NEGATIVE OF THE SLCEE OF THE CUEVE S2 BETWEEN ADJACENT 
POINTS ON THE CURVE - IF SiJ IS CFF-CUEVE, KOFFC IS SET 
EQUAL TO 1 . IF HJ IS EXACTLY CN A POINT. THE SLOPE OF THE 
SEGMEET TO THE LEFT (DECREASING DEFORMATION) IS USED 
FOB JOINT-SUPPOHT AND SESBER-SUPPOST CURVES, SEPARATE 
SUBROUTINES HAVE BEEN BEITTEN TC ACCOUNT FOB THE INELASTIC 
(HISTORY DEPENDENT) BEHAVIOUR 



COMES 

COM MO I 

COMMENT 

COMMENT 

COMMENT 

COMMENT 

COMMENT 

COMMENT 

COMMENT 

COMMENT 

COMMENT 

COMMENT 



- A SPECIAL SUBROUTINE IS ALSO BEITTEN TO PEBFCF.H A SIMILAR 



HISTORY DEPENDENT ANALYSIS OF 
BUT aiTH SOME LIMITATIONS FCB 

IMPLICIT REAL*8 (A-H.O-Z) 

DIMENSION QQ(11), 



2100 
2200 



3C40 



3045 
3050 
3 055 



IF 
GO 
SJ 



NEG 
(ISYM .EQ. 
TO 2200 



-H.O-2) 
80 (11) 



SIBESS-STBAIN CURVE, 
THE PRESENT 



1 .AND. HJ -LT. 0.0) GO TC 2100 



IJ 
NEG = 
CONTINUE 
DO 3040 NP 

IF 
CON 



1 



TINUE 



2, NPT 



»W(NP)) 3045,3055,3040 



GO 

IF 



IF 



HP = NPT 
TO 3050 
(KJ - 88(1)) 3050,3055,3055 

KOFFC =1 

NP = NP - 1 

S2 = - (QQ(BP + 1) - 

4J = WQ(NP) - S2*(BJ 
(KEG . £Q. 0) GO TO 4300 



s=isft^/" f t»» 



+ 1) - BW (NP) 



********** 
07963 
07964 
07965 
07966 
07967 
07968 
07969 
07970 
07971 
07972 
07973 
07974 
07975 
07976 
07977 
07978 
07979 
07980 
07981 
07982 
07983 
07984 
07985 
07986 
07987 
07988 
07989 
07990 
07991 
07992 
07993 
07994 



303 



4300 CONTINUE 
BETUilN 
END 



07995 
07996 
07997 
07998 
07999 



^^^ru^mmr:mum¥!^n^^ir^^^^ 



2 
CCHHENT 
C 

c 

c 



5?^ E 5 S SIGHIS, AND STIFFNESS STFHIS AT THP Ttr BT«ru 

SS s iSi°?foSi lid^F" I » A " ^l I gg H A I D iB!vlgi D H ifiiB only 

IMPLICIT EEAL * 8 (A-H ,"o-Z) 
DIMENSION SI3BI5(2), STFHIS (2) 
DIKENSI03 EPSCOMJl6f # SIGCOhIiO) 



"'"TTl'/?nr w "" / ™o?i£?' 6) # s « c (50,21), 1ST (50) . 



LT(50), 



coaaoN /BIKV tol, si.zavs.sas's. keep3c„nCd3c 

a ^?5£,KEEP5C # KEEP5d;kEEP6/keep7,NCD2; 'nCD3A ' 

5 NCD5D' NCD6 A ' ^^ E ' ?gg" C ' ?SS 5A gCBSfi, NCD5C 

| jfSfc lips, n1? 7 - 511; HI: n!t°- m" tjpe - 

7 C 0aa uN /gjfli/ .gLni^il.,^ "rf«JSS; SsTL 

CGfiHON /BLK7/ INLOPI, IFAE.KCFFJ KOFFOB *nvv<zv 
2 CQUQ»AtV l8Ji>fii«>i!fiP%KCSfESS1S0) ,«J<20) .MITF. 

COIiaOH /NIT/ APB08 

§8888! fslT% S5Wi»fi.if3J«1S«1,,0.3. 

fco««oii /skti 4 / xbvP^s 21 to;3{; E PBT 2 s(i];]o°;il' 



IBVBSE, 
CCMKON /SKT15/ JJ 
COMMON /SKT18/ SCHECK 
COEHOS /SKT22/ TIME, JT 

2 5 FCfi 

2 9 



ITAPE, 



FfcHCLD(50,6), 
N J 



IBDYN, IBSTEP(71) 

ELEMENT = ,13, 



bub /oaxz^/ Tin is, JT, IEDYN. IESTF.P 
MON /SKT33/ NKGIOH (21,2,10) 

gATA 3HsA f /53SHEAE/ 



NHINGE 



IF (ELEflNI 
DO 2u00 L = 



IF 
IF 



( L .EC. 

■. L .EC. 

IF | IB ,f5 

IF ( IB ,e3 

STB ESS 

STIFF 

DO 1200 K = 

SLOPE 

IF ( L . NE 

EE = 

EBT = 

GO TO 200 

100 CONTINUE 

EB = 
ERT' = 
2 JO CCNTIKUE 

IF ( DABS ( 

STIFF 
SO 
. NCEECK 
COflfiEJiT - ONLY FIBST 
K 

NfeGlCN 
IBV ( 
O 1400 
INUE 
NG ITEB 
S INTO 
E. IN S 
EBLY BE 
NZOUSIY 
E THE F 
EBT = 
IFAE 
S 

NEGICN 
INUE 



1 
.BE. 

'I 
.V 

. 1 
= 
= 

1 A N 
= SI 

1 ) 

EPE1 
EPET 



SAB) 

SE 

SAIN 

2AIN 
IE 



SHE 
KING 

STB 

STB 
.OB 
.OB 
.0 
.0 

PTSH 
GCOM 

GO 
S (I.. 
1S (I,ICUKO 



KHINGE=2 

= EP - CUE 1 * 1 

= EP - CUB 2 * X 

EQ. 1 ) STIFF 



IE .EQ. 1 j GC TO 1250 



"K)^ BMCOa(K) 

,ICUHU,K) 
-,K) 



SLPHAX 



EPB2S (I,ICUHU,K) 
PBT2S (I.ICUMU^K) 



STGAIN-EB] l .GE. (EPSCOM (K) -5. 0D- 10) ) GO TO 500 
LINEAfi ZONE ( BEGIN ) ' ' 



450 

CCflHE 
COMBE 

ccaaE 

COfiHE 
COM HE 
COKME 



IF i 

■ T - ONLY 
IF ( 
IF I 

GC T 
CONT 
NT - DUEI 
NT - HIDE 
NX - BANG 
NT - PEOP 
NT - EEBO 
Nl - HENC 



= STIFF + SLCPE 
= SLOPE *(SIEAIN-EB) 
■EE. 1 ) GO TO 450 
EST NE 



COMPONENT HEED q TC 5 BE MCNITOSED FOB BEVEBSAL. 

ij'ii^sta ) e = q -i° ] Go To 45 ° 



460 



IF 

IF 

CONT 



ATICN 
PLASH 
UCK A 
-FIXED 

USEE 
OLLCil 
EB 

EQ. 1 
NE. 1 
(I, L.I 



GO TO 1000 
500 CONTINUE 

IF ( STRAIN 

IF ( NCHECK 
IF ( K 



PBCCESS IT IS POSSIBLE THAT THE STRAIN 
C RANGE. AND THEN COMES INTO THE ELASTIC 
C $S E *»?,fe TE F2S AEY 3ESIDUAL STRAIN MUST BE 

i5 H TlE 1 giiT S ?aSiiI fl f HPB0PEB VALDES AflE N0T 

NG STATEMENT 

) GO TO 460 
I GO TC 460 
CUMU) = 

LINEAB ZONE ( END ) 



.SI. EE ) GC TO 600 

C t-£££ A ^ VE YIE L0 ZONE ( BEGIN ) 
— ilijCOd ( K) 
. NE. 1 GO TO 550 
. NE. 1 ) GC TO 550 



*********** 
08000 
08001 
08002 
08003 
08004 
08005 
08006 
08007 
08008 
08009 
08010 
08011*79 
08012*61 
08013*61 
08014*61 
08015*61 
08016*61 
08017*61 
08018 
08019 
08020*88 
08021*88 
08022 
08023 
08024 
08025 
08026 
08027 
08028 
08029 
08030 
08031 
08032 
08033 
08034 
08035 
08036*78 
08037*78 

08038*78 

08039*78 

08040 

08041 

08042 

08043 

08044 

08045 

08046 

08047 

08048 

08049 

08050 

08051 

08052 

08053 

08054 

08055 

08056 

08057 

08058 

08059 

08060 

08061 

08062 

08063 

08064 

08065 

08066 

03067 

08068 

08069 

08070 

08071 

08072 

08073 

08074 

08075 

08076 

08077 

08078 

08079 

03080 

08081 

03082 

08083 

08084 

08085 



304 



550 



C 

c 



560 



GO 



600 



650 



660 
'1000 



CONTINOE 

?! f ae *s§* n go tc 56 ° 

IF ( K - NE. 1 i GO TC 560 

NfiGICN(I,L,ICUBU) = -1 
CONTINUE J 

I0 1000 NEGATIVE YIELD ZONE ( END ) 

SO = SIGCOfl-? IVE IIELD ZCNE ( BEG1N > 
IF ( NCHECK 
IF ( K 
IF ( NBGIOt 

IB! 
GO TO . . 
CONTINUE 

EKT = STBAIN - EPSCOHJK) 
IF IFAE .20. 1 ) GO TC 660* 
IF ( K , HE. 1 } GO TC 660 

NaGICN(I,L # ICUtiD) = +1 
CONTINUE 

„„„«,„ POSITIVE YIELD ZCNE { END ) 

STBESS = STBESS ♦ SO l ' 

IF ( L . BE. 1 ) GO TO 1 100 



nm 



= STBAIN ■ 
.EQ» 1 ) t 
. NE. 1 j C 

:n(i,l,icui 

NEGA1 

„. POSITIVE YIELD 
= SIGCOH(K) 

:K ,BS, 1 J GO TO 650 
. NE- 1 ) GO TO 650 
J8SI0N(I,L,ICukn .NE. -1 
CSV J 1, L, IC.UHD ) = 1 
I 400 



) GO TO 650 



C 

c 

c 



, ,.„ GO TO 1150 

1 100 CONTINUE 

EPB2S 



1150 CONTINUE 
1200 CONTINUE 



EP21S~ a,ICUHU;K) "=~E2 
EPET1S(l,ICUHU,Kj = EBT 



(I,IC3BU,K) = EE 
EPHT2S(I,ICUHU,K) = EBT 



1210 



1220 




FORHST 

BEMSOL 



■EC. 1 ) GO TO 1220 



1210 

1250 
COMMENT 



-«, „ , _ CKLy IN STATIC ANALYSIS 

IFAE=1 THIS SUBBOUTINE IS INSIDE 
THIS SUBBOUTINE IS INSIDE 
ITYPE ,GE. 3 ) GO TO 1210 
.EQ. 1 ) GO TC 1220 
•EQ. 2 .AND. NITEHH(JJ) 

CONTINUE 

IF ( IfiDYN .EQ. 1 ) GO TO 1220 

U I ^ I fy^ T, * Ea - 1 - AND - NITF - E 2.1.AND.NITEEM(JJ).EQ. 1)GO TO 

CONTINUE 

IF { IBV(I,L,ICDHU) .Efi. ) GO TO 1250 

STIFF = SLPHAX 
IF ( ITYPE .LZ. 2 ) GO TO 1240 
T H x i3S yH - E0 -- 1 ) GO TO 1250 
IF (IfiSTbP 7 JTji. EQ. 1 . JND. NITF.EQ. 1. AND.NITEBH (OJ) . EQ. 1) 

GO TO 1250' ' 

CONTINUE 

CONTINUE 2 ' ES * ° ' "'(^I'lCOflO) = 



~WtZ 1 §,* S T , IF L fG2 BIGID E1EHENT 
if ( J| -EQ- 1 ) STIFF = 10.0 * STIFF 

GO TO 14oP Q " ,0B * IE ,EQ * ' > GC T0 1300 
1300 CONTINUE 

1400 CONTINUE ^^ ' S%lf? * SIBAIK 
SIGHI3 (L) = STBESS 
STFHI5 ?L) = STIFF 
COMMENT - OUTPUT HESSAGE (DURING FINAL BEBBES SOLUTION ONLT1 TP tru 
COfiBENT - STRAIN EXCEEDS THE LAST STRAIN CHDINATE OF VIBGIN 1 CUBVE 

HNITH+2 ) GOTO 1500 "■ LaK ' J - a v-uavc. 

GC E TO1^00 TSM1) > G ° T ° 15 °° 
,:;., ?HIN ? 2| is JJrI,L;iCUHU,STKAIN,SIGHIS(L),STFHIS(L) 

GO TO 2000 




1800 CONTINUE 
2000 CONTINUE 

BETUBN 

END 



IF ( In .£u. 1 .OB. IE .EQ. 1 ) GO 
IF j NCHECK .NE. 1 ) GO TO 180D 

IHVfiSE = IBVRSE + IHV f I, L. 



ICUHD ) 



08088 
08089 
08090 
08091 
08092 
08093 
08094 
08095 
08096 
08097 
08098 
08099 
08100 
08101 
08102 
08103 
08104 
08105 
08106 
08107 
08108 
08109 
08110 
08111 
08112 
08113 
08114 
08115 
08116 
08117 
08118 
08119 
08120 
08121 
08122 
08123 
08124 
08125 
08126 
08127 
08128 
08129 
122008130 
08131 
08132 
08133 

08134 

08135 

08136 

08137 

08138 

08139 

08140 

08141 

08142 

08143 

08144 

08145 

08146 

08147 

08148 

08149 

08150 

08151 

08152 

08153 

08154 

08155 

08156 

08157 

08158 

08159 

08160 

08161 

08162 

08163 

08164 

08165 



~*7^T*iinf-_£oTrp 



C0H3ENT 

C 

C 

C 

C 

c 
C 
C 



SHALL, SBHO.SiaD.SDIT. ALP. BET 1 
oTthFcIoII sld^f f T Z ' AKE ^ ^UB^IV^D^llcE 



08168 
08169 
08170 
08171 

lUkl^lUWU¥nin IfllL 1 " DEGHAEAI "« COB YIELD GBOiTH 8 1 j | f 
^ , Sn 3A ' r F^ A J; S -,? THEfi THAS "" STEEL, THIS SUBBOUTINE CAN 0817S 
HANDLE A GENERAL SSTKBETBIC VIBGIN CURVE , WITH A PpJsCBIBED 08176 



305 



DEGREE OF DEGEAIATION ONLY 



C 

C 

c 



HOIIELD GBOHTH > 

CAN A1SC HANDLE 
TIELD GBOHTH ) , BUT 
SBPEBATE SUBROUTINE 



3(2). SIP 

ihb\, si 

FCah(50,6) ,SaC(50,21) ,IST(50) , 
JT2 50) , NITB(50S. IBM(SO), 

., JOL. ELSHNT,NJST, KEEP3C, NCD3c! 
Ife K?F3A,KEEP3E,KE£f4A,KEEPi;B;KEEP4d,KEEP5A, 
5E,KEEP5C,KEEP5D, KEEE6, KEEP7, NCD2, NCD3A. 
1R. Krnui nrrv/io Brnlr' umci' n^.XPi ;;„_??„' 



IT (50) , 
iafc(50) 



TEIE MASING MODEL ( nS DEGRADATION, NO 

IS NOT ECONOaiCAL TC DO THIS. HENCE A 

IS WRITTEN FOE THE BASING MODEL. 
IMPLICIT REAL * 8 ( A-H, 0-Z ) 
DIMENSION SIGHIS(2), STFHIS (2) 
DIMENSION EPSCOBMD), SIGCCKMO) 
2 COaMO|^3LOCKV |CaM50,6) ,SBC(5 

COHHON /BLkI/ TOL 

2 KEEP2 

3 KE2P5_ 

I »CD3B,-SCD4A, "HCDiJB," NCE4C; NCD5A; NCD5B, 
5 NCDaD, HCD6 f »CD7, IP8 r IP9, IP10, 
b lABAS, IFCfifi, m, KJT,' NST,' BIT, 

'common Alky ^Ih^ftl^ 1 ' "*«".MJ: 

COMMON >flLK7/ INLOPI, IFA2, KCFFJ.KOFFQS . KOFFSE 
2 COMMOt,/ITC/ ggai.EB|J,EBi:EB2,D4l f CH; 1 ltl,HH(20).HJ(20) r HKITF. 

COMMON / NIT/ APBSB 

COBKON /SKT6/ NITERM([50) , INDEX 

^COaaOH /SKT13/ EPSlS(21,l5,3) ,EPBT1S(21,10,3) , 

FOBOLD(50,6), 



NCD5C, 

ITYPE, 

NSTL 



CGHKON /SKT14 / IEV (2 1, 2, 1 Of , 

2 IRVESE, IIAPE, 

COKfiON /SKT15/ JJ ' 

COMMON /SKI 18/ NCHECK 
COaaON /SKT22/ TIME. JT, IEDYN, IBSTEP(71) 

** EPSMAX (21,2,10 

5„„ IGEOH (21,2,10 

. COHflON /SKT33/ NBGICN (2 1^2^10 
D FORMAT ( 18H **NOTE** BEBBEB = .I4,MH, 

2 98, HiNGE =,12, 9H, PIECE =,13,/, * 

3 10H STEAIN = ,1?E10.3./, 9H STRESS =,1PE10 

4 12H STIFFNESS = .1PE10.5) ' 



N3 



EPBFT1 

EPBF2 

SLBFT2 2i;i0,3 

£PSBIN(21,2, 10 

YTGBOW(21,2,10 



SLBF1 

EPBFT2 



(21,10,3) 
(21,10;3) 



, EPSPBE(21,2,10) 



ELEMENT = ,13, 
3,/. 



IF 
DO 
IF 
IF 
IF 



DATA SHEAE /5HSHEAB/ 
E = 1 



NHING 
(ELEMN1 
2000 L = 

L . EQ. 

L . E Q. 

IE .EQ 



■ NE, SHEAJ2) 
1,NEINGE 



NHINGE=2 



1 



STRAIN 

STEAIN 

•OR. IE 



= EP - 
■ EP - 
.EQ. 1 



C0B1 * Y 
CUR2 * Y 
) STIFF = 



SLPBAX 



( IS .fa, 1 .OR. IE 
( BODEL1ISTT) .NE. ; 



ilSTT) .NE. 
= YGECS 



55 



(i,i,icuau) 

YTGEO«(I,L,ICOMD) 



50 



IF ( IS . E 
IF ( MODEL 
YGH 
ITGR 
CONTINDE 

STEESS = 0.0 
STIFF = 0.0 
TEMP9 = EPSMAX 
TEMPO = EPSMIN 
1200 K = 1.NPTSM 
( TE3P9 .LI. EPSCOM 
( TEHPO .GT.-EPSCOB 
SLOPE = SIGCOM(K) / 
BET .GT. 1.0D-T5 ) SO 
IGR = SIGCOM(K) 
„ „ YT5R = SIGCOB K) 
CONTINUE 

IF ( L .NE. 1 ) GO TO 
= EPS1S 
= EPRT1S 



.EQ. 1 
) GO ' 



A IS 



TO 1250 



DO 
IF 
IF 



IF ( 



(i,l,icoso) 

|l,L,ICaM0) 



/ EP 



TEBP9 = EPSCOB (K) 
TEMPO =-EPSCOM(K) 

SCOBfK) l ' 

TO 60 



C 

c 
c 



100 



200 



EFBF1 
EFBFT1 
SLBF1 
SLBFT1 



EPB2S 

EPRT2S 

EPBF2 

EPBFI2 

SLBF2 

SLBFT2 



100 

i,icoao,K) 

I,IC0BD,K) 
I,ICUMn,K) 
I,IC0M0,K) 
I,IC0MU,K) 
I,ICUM0,K) 



I,ICUB0,K 
I,ICDHU,K 
I,ICDM0,K 
I,ICOB0,K 
I,ICDBU,K 
I,ICUBU,K 



310 



EK 

EET 

EPBFE 

EPBFfil 

SL3FB 

SLBFET 
GO TO 200 
CONTINDE 

£R 

ERT 

EPEFE 

EPBFET 

SL3FE 

SLBFET 
CONTINUE 

REFER FLOB CHART OF FIGURE 3.4 OF 
"OUT THE EEGIONS MENTIONED BELCS 
REGION 1 ( UPTO STATEMENT # 320 

TEHP9 .GT. EPSCCM(K) ) 

TEMPO .LI. -EPSCOB (Kj J 

YTGE = SIGCCM(K) 

STEAIN. GT. EPSCOB (K) ) 

STEAIN. LI. -EPSCCE K) 

NCHECK . NE. 1 ) ' 

^ JJ£ "J j 

NRGICN(i,L*ICUHU) ,£Q 
IRV (I,L,ICUKU) = 1 
TO 1400 

CONTINUE 

20 = SLOPE 



08177 

08178 

08179 

08180 

08181 

08182 

08183 

08184 

08185 

08186 

08187*79 

08188*61 

08189*61 

08190*61 

08191*61 

08192*61 

08193*61 

08194 

08195 

08196*88 

08197*88 

08198 

08199 

08200 

08201 

08202 

08203 

03204 

08205 

03206 

08207 

08208 

08209 

08210 

08211 

08212 

08213 

08214 

08215 

08216 

08217 

08218*78 

08219*78 

08220*78 

08221*78 

08222 

08223 

08224 



)§; 



IF 

I? 

IF 
IF 
IF 
IF 
If 

GO 



I 



GO 

GO 



GO 
GO 



) 



TO 
TC 

TC 
TC 
GO 

GO 
GO 



DISSERTATION FOR DETAILS 
IN THIS SUEEOUTINE 

32 
320 



32 
320 
TO 310 



TO 
TO 



310 
310 



5^ 

UQZ2 o 

8227 

08228 

08229 

08230 

08231 

08232 

08233 

08234 

08235 

08236 

08237 

08238 

08239 

03240 

08241 

08242 

08243 

08244 

08245 

08246 

08247 

08248 

08249 

08250 

08251 

082 52 

08253 

08254 

08255 

08256 

08257 

08258 

08259 

08260 

08261 

08262 

08263 

08264 

08265 

08266 

03267 

08268 

08269 

08270 

08271 

08272 



306 



315 
317 

320 



331 



C 
C 



340 



343 

344 

34c 



350 



356 



C 
C 



364 

380 

2 
387 

390 

396 



405 



411 



iLfet = mu * sibaib 

IF ( STEAIN .LT. 0.0 ) GO TO 315 

EPBFET = EPSCOH(K) 
GO TO 317 
CONTINUE 

EPEFET = -EPSCCB(K) 
CONTINUE 

IF I IFAE .£Q. 1 1 GO TO 484 
IF { K .Jig. l GO TO 484 

NSGICN(I,L,ICUBU) = 
GO TO 484 
CONTINUE 

if ( (STBAIN-EPBFR) .LT.-1.0D-15 ) GO TO 405 
REGIONS OF POSITIVE VELOCITY 



IF I NCHECK .HE. 1 ) 
I| ( K .HE. 1 
IF ( NBGICN(I,L,IC0HU) , 
IEV<I,I,ICDaU) = 1 
3 1400 ' 



.HE. -1 ) 



GO TO 331 
GO TO 331 
GO TO 331 



.LT. 



GC TO 396 



. Efi ) 
9 . 2 AMD THEIB PBIM.E 



GO TO 

CONTINUE 

IF ( STEAIN 

REGIONS 8 , 

IF ( EPBFE . Ot. EE } GC TO"3 

REGION 8 FOLLOWS FBOH BEGIOK 7 . 

IF ( BET .LT. 1.0D-15) GC TO 3 

GBOBTH IN THE YIELD STRESS LEVEI 

IF I TEMP9 -GT. EPSCCB(K))GC TO 3 

IF ( TEMPO . LI.-EPSCOfl(K) GO TO 3 

YTGB = SIGCOfl(K) 
GO TO 346 
IF ( TEaP9+TEBP0.GT.0.0) GC TO 3 



YTGB 

GC TO 344 

YTGB 

IF ( YTGE 

YTGB 

E0 = 

SO = 

GO TO 356 

E EG ION 8, 



D EQUIVALENTS 

SO ESTABLISH BEGICN 8 

46 

IS EFFECTIVE NOB (NEXT 10 

40 

40 



43 



SIGCOH(K) ♦ BET * SLOPE * TEBP0 * TEHPO 



■ SIGCOB(K) 
LE. SULT 



BET * SLO 
) GC TO 3 



PE * TEHP9 * TEBP9 
46 



- SULT 
lo G "" ( STE^li P!£ C H(K) + ALP*(TEHP9-E5-EPSC0H(K)) ) 



, 9 Ofi 2 FOLLOWS 3« (OB 2 
E0 = SLBFE V 

SO = SLOPE * (EPEFfi-EB ) + S 
YTGB = YGE 

IF { DABS (SLBFB-SBALL) . LT. 1.00 

IF I SLBSk .LT. 1.0D-15 ) 

CONTINUE ' 

CHECK IF CVEBFLOW INTO BEGICN 9 ? 

ElTlB!§SH L lE G !^e fi<K) > GC T038 ° 
IF ( £0 .LE. 1.00-15 ) GC TO 3 64 

Z = STEAIN - ( SO - SIGCCB(K) ) / EO 
( DAES(TEKP9-Z) V .LE. 1 . 0-15 7 GO TO 364 

SO = YTGE - SIGCCH(K) ) / ( TEBP9 - Z 

CONTINUE = SIGC0B < K > + E0 * < ^IaIn - F ) 
CHECK IF OVESFLOH INTO BEGICN 2 ? 
IF ( SO .11. YTGE ) GC TO 380 
ESTABLISH REGION 2 

l°n = H G fr + SBA " * ( STBAIN - TEHP9 ) 
tU = SBAL1 

?S EC 7 K „iL S0N0T0I,IC EX COBS ION INTO +VE STEAIN 
If YTGB .GT. SIGCOK(K) ) GO TC 387 

IF j STEAIN .LT. EPHD ) ' GC TC 387 

FOLi,Oii_ + VE 3EANCH OF VIRGIN STEAIN HABDENING 



FOLLOWS 3) . USE STOBED VA 

LBFB * { STEAIN-EPBFH ) 

'-15 ) GC TO 380 
GO TO 380 



IF 



HABDENING 



EO 

SO 



= SLHD 

= SIGCCM(K) 



IF 
I 



M 



.LI. SUIT ) 
= SOLT 
= 0.0 

STEAIN 
EO 
, 1 ) GO 
1 ) GO 



SBALL 

SLH 



LL * ( 

D * i 

GC TO 



IF ( SO 

SO 

EO 

EPBFET 

SLBFET = 

IFAE . EQ 

K . HE 

NSGICN(I,L,ICUHU) 
GO TO 484 
ELASTIC EEGION 7 ( OR 7« 

EO = SLOPE 

SO « SLOPE » ( SIEAIN - EB ) 

EPBFET = EPBFE 

SLBFET = SLBFE 

YTGE = YGfi 



EPHD-EPSCOB(K) ) 
SIEAIN-EPHD ) 
390 ' 



TC 484 

TC 484 

= +1 



) 



IF 

IF 



IFAE .BO. 1 ) 

K . HE. 1 ) GO TC 484 



GO TO 484 



NHGICN(I,L,ICUMU) = 6 
GO TO 484 
COSTINOE 

REGIONS OF NEGATIVE VELOCITY 
IF ( NCHECK -BE. 1 ) 
IF ( K .HE. 1 ( 
IF ( NBGICfl (I.L.ICUaO) .HE. +1 

IEV (I,L,ICUMU) = 1 
GO TO 1400 
CONTINUE 
If ( SB .LT. STBAIN ) GC TO 



GO TO 
GO TO 
GO TO 



411 
411 
411 



476 



Q8273 
08274 
08275 
08276 
08277 
08278 
08279 
08280 
08281 
08282 
08283 
08284 
08285 
08286 
08287 
08288 
08289 
08290 
08291 
08292 
08293 
08294 
08295 
08296 
08297 
08298 

ST) 08299*90 
08300 
08301 
08302 
08303 
083 04 
08305 
08306 
08307 
08308 
08309 
08310 
08311 
08312 

LUE08313*90 
08314 
08315 
08316 
08317 
08318 
08319 
08320 

81131 

08323 

08324 

08325 

08326 

08327 

08328 

08329 

08330 

08331 

08332 

08333 

08334 

08335 

08336 

08337 

08338 

08339 

08340 

08341 

08342 

08343 

08344 

08345 

08346 

08347 

08348 

08349 

08350 

08351 

08352 
08353 
08354 
08355 
08356 
08357 
08358 
08359 
08360 
08361 
08362 
08363 
08364 
08365 
08366 
08367 
08368 



307 



c 
c 
C 



420 

423 
424 

426 
430 



436 



444 

460 

2 
467 

470 
476 



434 

500 
600 

650 



1 100 



1150 
1200 



GC TG 420 



IITIIbSb' ^LT.Sb"? IHE ^ ^«f D EQ0I7A1ENJS 

fFTfci f2E°!!o33i I - I§ ig T HP H BEGI0N • 

IF { TEMPO .IT.-EPSCQbM) 

TTSB = SIGCOM(K) 
GC TO 426 V ' 

IF ( TEMP9+TEMPG ,81. 

YTGE = SIGCOH(K) 
GO TO 424 

YTGB = SIGCOMfK) 
IF ( YTGB .IE. SULT 

YTGB = SUIT 

EO 

SO 
GO TO 436 

EO 
BEGION 4, 

SO 

YTG2 
IF 
IF 



0.0 ) GC TO 423 
+ BET * SLOPE * 

+ BET * SLOPE * 
GO TO 426 



TEMPO * TEMPO 
TEHP9 * TEMP9 



= io G *°Vs^iiN P - C EH < f ) +Alp *< M - ;EPS coH(K)-MaP 



I S 
1TIN 



= SLBFE 

5 OB 6 FOLLOWS 7" 

= - (SIOP£+(EE-EPBFB) ♦ 

M^f^f^'f^^U'P- 1 -0D-15 ) GO TO 460 
SLBFE .IT. 1.0D-15 ) GO TO 460 



JOB 6 FOIIOBS 7). USE STORED 
SLBFR+ (EPBFB-STBAIN) ) 



CONTINUE 

CHECK IF CVEBFLOW INTO BEGION 5 ? 

JL,JL S0 * G2 - -SIGCOH(K) ) GO TO 460 

ESTABLISH BEGION 5 

IF ( EO .IE. 1.0D-15 ) GC TO 444 

Z = STBAIN - ( 50+SIGC0H(K) ) / EO 

IF ( DABS (TEMPQ-Z) V .LE. 1.0D-1!')'g6 TO 444 
EO = YTGB-SIGCOB(K) ) / ( Z-TEHPO ) 
SO = -SIGCCM(K) + EO * (STEAIN-Z 1 

CONTINUE ' " * ' 

CHECK IF C7EBFLCK INTC BEGION 6 ? 

If t SO .61. -YIGR ) GC TO 460 

ESTABLISH BEGION 6 

EO = SMALL * SaALL * ( STSAIN -TEHP0 ) 

IF (STBAIN . GT. -EPHD [ GC TO 467 

rOLLOW -V£ B2ANCH OF VIEGIN STBAIN HA2DENING 

SO = -SIGCCfl(K) - SHALL * ( EPHD - EPSCCfl(K) ) 

IF ( SO .«. -SUIT ) gVtoVo l SIEAIN + £PHD > 
SO = -SULT 



IF 
IF 



EO = 0.0 
EPBFET = STBAIN 
SIBFBT = EO 



( IFAE . EQ. 1 ) GO TC 484 

( K . HE. 1 j GO TC 484 

NEGICN (I.I.ICUBU) = -1 



GO TO 484 

EIASTIC EEGION 3 { OB 3 • ) 

EO = SLOPE 

SO = SLOPE * 

EPBFfiT = EPBFB 

SLBFBI = SLBFB 

YTGB = YGB 



( STBAIS - EB ) 



{ IFAE .EQ. 1 ) GO 10 484 

( K . m. 1 ) GC TC 484 

NEGICN (I, L.ICUHU) = 



IF 
I? 

SET THE VALUE OF THE TEMPOBABY EESIDOAL STBAIN . 

ESI = STRAIN - SO / SLOPE 
IF ( IFAE .EQ. 1 ) GO TO 500 
IF ( K . BE. 1 ) GO TO 500 
IF (DABS(EU-SICEE) . GT. 1.0D-05) GO TO 500 

NBGICN(I,I,ICUHU) = 



CONTINUE 

STHESS = SIHESS * 
STIFF = STIFF + 

CONTINUE 

IF ( K .HE 

IF ( i 



SO 
EO 



[SIT 



MODEL (ISIT) .HE. 2 ) 



1 I GO 10 1 100 
I.ICUMU.K 



GO TO 650 
GO 10 650 

YG50W (I, I.ICUMU) = YGB 

YTGRC* (I,I,ICUMU) = YTGE 
CONTINUE ' 

IF ( I .NE. 

EPS1S 

EPRT1S 

EPBF1 

EPBFT1 

SLBF1 

SIBFI1 
GO TO 1150 
CONTINUE 

EPS2S 



I.ICUMU.S = 

i,icuau,K = 

I.ICUMU.K = 

I.ICUMU.K = 

i.icaau.K) = 



EB 
EST 

EPEFB 
EPBFET 
SLBFB 
SLBFBT 



il.ICUMO.K) = EB 

I.ICUMU.K) = EST 

I.ICUMU.K) = EPBFB 

I.ICUMU.K) = EPBFET 

I.ICUMU.K) = SLEFB 

I.ICUMU.K) = SLBFHT 
LUaii»U£ 
CONTINUE 



08369 
08370 
08371 
08372 

10 ST) 08373*90 
08374 
08375 
08376 
08377 
08378 
08379 
08380 
08381 
08382 
08383 

0) ) 08384 
08385 
08386 
08387 
VALOE08388*90 
08389 
08390 
08391 
08392 
08393 
08394 
08395 
08396 
08397 
08398 
08399 
08400 
08401 
08402 
08403 
08404 
08405 
08406 
08407 
08408 
08409 
08410 
03411 
08412 
08413 
08414 
08415 
08416 

Qgit 1 7 

08418 

08419 

08420 

08421 

08422 

08423 

08424 

08425 

08426 

08427 

08428 

08429 

08430 

08431 

08432 

08433 

08434 

08435 

08436 

08437 

08438 

08439 

08440 

08441 

08442 

08443 

03444 

08445 

08446 

08447 

08448 

08449 

03450 

08451 

08452 

08453 

08454 

08455 

08456 

06457 

08458 

08459 

08460 

08461 

08462 

08463 

08464 



308 



IF f {TYPE .SB. 3 ) GO TO 1210 naiifi^ 

IF I IFAE ,EQ. 1 50 10 1220 fiHUfiS 

cl L 1?L' EQ - 2 ASD ' NIIES B(JJ) -EQ. 1 ) GO TO 1220 08467 

1210 CONTINUE 08468 

IF ( IRDYN .EQ. 1 ) GO TO 1220 OAU70 

"J TO T 12iO T) - EQ ' 1 * ABD> MIT *' E 2- 1 • AHD. NITERB (JJ) . EQ. 1) GO TO 12200847 1 

1220 CONTINUE Sin?? 

IF ( sm-isi * ec - ° > go to 125 ° §§«i 

JU Jlfi ;ft ? I SS to !2§8 

IF(IRSTEP JTf.EQ.1.AH0.NITF.EQ.1.ASD.NITEBH(JJ).EQ.1) 08478 

GO TO 1250 '* 08 ' t79 

1240 CONTINUE 08480 

1250 8^i55i E - EQ » ° » «*(i.i.icuho) = o 8|jy 

COHflENT - STIFF = 10 * STIFF FOB BIGID ELEflENT 0848a 

II ?S *l a * 3 ST ' lyF " 10 '° * STIFF 08485 

SS io^uaS"- 1 - 0fi * IE - EQ - 1 > GC T0 1300 B|||f 

1300 CONTINUE 2fS§2 



STRESS = STIFF * STRAIN 



08488 



1400 CONTINUE*" " »"" * iXBAIK S§»§1 



08490 
08491 



SIGHIS(L) = STBES 

STFH13JL) = STIFF nn/io-i 

COMMENT - OUTPUT MESSAGE (DUEING FINAL HEBBEB SOLUTION nuTTl TP tup nSJ^ 

STEfiP = SIGC0HO) + ( EPHD-EPSCOBM) ) * SHALL ORUqfl 

EPULT = EPHD ♦ { SULT-STEBP)/ SIHC BBAii ohuqq 

IF ( DABS(STSAIN) -IT. EPULT SO TO 15^0 fts^nn 

PEIN GO T6 ^6^ L ' ICu{5U ' SIfiAI »^IGHIS(L),ST!HIS(L) 0°8501 

1420 CONTINUE 08502 

u himv^n i l ?-gPt s 8°^oT shi) > go to 150 ° S!|§l 

1500 PfiI ^ NTiNU2' I ' L ' ICDH0 ^ TfiAIN ' SIGHIS(L, ' STFHIS(L > 08506 
IF f IH~. EQ. 1 .08- IE -EQ. 1 ) GO TO 2000 OaSOfl 
IF | NCHECS . NE. 1 ) GO TO 1800 OflSOq 
laVfiSE = IEYBSE + IHTfl.l.ICDBDI naiV.n 



1600 CONTINUE 



2u00 CONTINUE 

BETDBN 
END 



E?SPRE(I,L,ICUHU) = STRAIN 08512 



08512 

89311 

08515 



sTIIT: Mf '' B "' 6 " c ' 6 ' 6 ' Hi 

C(I,J) = 08522 

„ Od Ss'k = 1,N1 08523 

ff SiifiA" i(I ' K >* B < s ' J > + C < I - J ) §Sli§ 

81i£$ 

"""^"inTs^l^ 

£822153 -' ItIu g ct e u^ h EiIIct?c 6 Is s5iff{,ess flMBIZ E0B aEflBEE SFBIH " » 81313 

IMPLICIT BiiAL*8 (A-H,0-Z) ffi30 

DIflENSION SA (3,3) ' 08531 

i cos ipf ■' l!IL|It; f mu-'sw. ww.- liw- hi 

5 SALf isP 1 ' ififtMff' ifi?S <,!?>» NC5 M 25 N I H "Pi 25), 08536*42 

SiSig: SgB« 4 *' Sg8«- £S§ c - II I; ||?| fi - I - 

6 IABAN, IFORM, bh MJl,' NSt! NLT,' «J ollftttJtl 

BSS = DC2S jISTT). **2 np^uT 

IHI = 3Cl2(ISTT)*EC2SfISTT) 08SUR 

|A(1,1).= ALS*SXT + BES*SY1 OflittQ 

SA(1,2J = ALBE*( -SXT + SYT) SiisS 



08550 



309 



SA (2,1) = SA (1,2) nacc, 

ft M =efH xi + al5* sxt Hill 

SA (3 2\ = 00 08555 

SA [i'A] = 00 08556 

EETUfiN 3AlJ ' c> J u -° 08557 

END 08558 

08559 



DIMENSION W(L6) ' S§lf 3 



i j^:Riyfl'iinW'ttfi:«aA; III 

08572 
08573 
08574 



ill?. I!. 1 fe fi if: < !• I <!- 



6 BH S{ 22) Blisf i*i ^i/^f ?£} S|(# DS (3,3, 22), 08576 

COMMON /koc'lV SEET 6,11' *" ( 221 ' 4G < 22 > °§577**S 

COMMON /ELK1/ TOL, ELEBNI, 

2 WW1 KVVb1\ v-1:ct«t>ti 



08578 



'B1KV TOL, BIEBHI.HJST. KEEP3C.NCD3C n«R7Q*7Q 

Sgli: ES^ Eg*. 8 - K c - !^ a; Mb III : 

b J ABAN ' IFOfifi, HH HJT,' NSt! KIT. H. ' OfiifluJfil 

CCPiOli /BLK$/ l? P |£ ti 1 !} 1 ' lTT » ^SPS 1 *™*! NSTL 08585*6 

lllill flftfiK gjSii ^',sia. ST 5,s?6 Ta ' HSQ ' Bc6 ' z2L ' 11 ' 12 '^ §1111 

COMMON /BLK5/ QT1»CT2,QT3,C , I4'CT5!0T6 nasfZ 

IAXOPT = IAXOPS(ISTT) uosyu 

£822133! " SS^!" 3 ? .INCfiEflENTAL ELEHElST-EHD-FOfiCES OH ELEMENT NUHBEB 2 Ofifl? 
COMMENT - BI USING 1HE OPPER HAIP OP SEEE(6,6) THAT MS STORED IB BLEHSI08593 

UT (l\ = i m 08596 

iol::j } - iIP sign 



DO 

SEE3 (I, J) = SEEE (I, J) 



100 CONTI l" li '° ; = B * fiJS lI **' off!! 



SSSSISi : SL L IL p c L I B !Ms a£ A N i 3H5HP I,5»»» TIflES "»"»« 0F H * a * E * 8I18J 

150 CO*Tlfu! I(I > = ™"™ 0||8| 

D ° "JmViVj 8if8$ 

DO 200 WT( J I, = = 1»i I " ) gflfl 

JP3 = J i 3 08610 

200 CONTlfu! 3 (I ' J) = SE£E »'*»> i|| 2 

3KHf^ffi|^ | E ||I|f m { «i'9^i1.iiai-HS- or »» 

DO 250 1=1 J : ' fi£J ' HT » ft!laT ) 08616 

250 CONTI^ I(I) " fMflI ^ * ""^ 03618 

ftSHii : iSx£PHfi l HftH, 8 i,H,iS" BAi foira M A ■a^B'kiHWWjfgj 

DO 600 I = 1,3 28623 

IPJM1 • 1 + 3*{M - 1) Sg? 2 5 

ram = w(iP3Mf) ' 9§§|i 

IP3 = I + 3 nfl£ 2 T 

DO 600 J = 13 98627 

600 CONTalil 3 *' J » ■ S££E < I?3 ' J > 629 

gSSSilig : gg?^I H fifI s K SSHf SiS AMn TIHES » c ™««* °* « E «^ 8 1 

CALL DO 650 h I T - 3 1 i SHE3 ' "' Fa " T) 08633 

IP3 = I i 3 08634 

650 CO,TI^E al(IP3 » =fMHT ^' 8§ ||i 

XP3M * I + 3*H 08639 

HT(I) = B(IP3H) ^Utl 



310 



700 CONTINUE 



DO 700 p3 J = = j 1^3 3 n 86ft; 

SEE3 (I.J) = SEEE (IP3.JP3) 08644 



COBMENT - MULTIPLY ELEMENT STIFFNESS KATHIX TIH^S INCPEHFNTS of mpmbur nafi»2 
COaHEUT - DISPLACEMENTS AT EIHST STATICS IH SIDE HEBBEfil"!?? ° F BEHBEB §fftt7 

""DO TSO^ 8 ! 1 ^ 3 ],^ 23 ' «• FBHT ' 086J8 

750 co N Jl lllIp3,+ ' "«(»3) tniim Sllil 

COaalli - END STATICNS MENTAL END_L0ADS AND INCREMENTAL SPRING FOBCES AT 08653 

FHSI(31 = FHBI(3) + ST3*Wj3) - QT3 08655 

_ FHBIJ6 = FHfll 6 + ST6*HT(3) - QT6 08656 

IF (IAXOPl .EQ. 2) SO TO 800 ' 08657 

FSai(1) = FMai(l) + ST1*8(1) - QT1 08658 

15 HI 23 = FS Ml 2 t ST2*SJ2[ - QT2 08659 

FB3I M = FHHI 4) + ST4*ST(1) - QT4 08660 

GO TO^SF 1 = fBHll5J + ST5 * HT{2 5 " « T5 gfffj 

CALL HAX3.31 SA^BT,FaEl[ 08665 

|aai(4) = T&klti) * FHHT(I) - QT4 08666 

Fgaxlsi = Faai 5 + mi 2 - QT5 08667 



bui = sis 

MT(3) = 0.0 



08667 
08668 
08669 



CALL SANGLE (SA,ST1,ST2) 03671 

CALL aATa31(SA,&T.FflflI)' 086T2 

FEMIJ1) - FHBI(1) + FHHT(1) - QT1 08673 

900 coMiSSi 1 ™ = fMBll2 5 * fMM ^ 2 5 - 8« o||B 

ff™ BN ol676 

tiiu 08677 



*****t**********t**^**/V********* SOBSOUTINE ********+*******+**********•**•**++ 

sUcKOOTINE FOE3LD ( Rfi, RO, SI, SL. FOHT. LI. L3 L4 16 7 "M n«ft7R*7u 

COMMENT - SUBROUTINE FORBID CALCULATES HEMBEB 'INCREMENTAL' FIXED-eId- 08679 

CCaaE^I - FORCE 3ATEIX ON FIRST ITERATION OF EACH PROBLEM 08680 

-LJafiiXl-X 1 nLAL'a (A"~fl, U— Z) Dft£ft1 

DIMENSION RB(L6,L4>, RO (L6) . W(L6) 08682*74 

DIMENSION FOai(S),Vf (3),FT(5) ,SA(3.3) 03683 

COMMON /BLOCK2; DXS( l 25)', DYS( l 2SV, ZLS ( 25), DC1S( 25), 08684*42 

2 3 JHfilaffi' ffltf&l. ™< 25 >' 2«<25), 1.(25). 81111531 

«»*( |5> l ' iUFiUZ?'* XPI»S{^gS> , HC5JJ 25} , INIOP^25) , 08687*42 



1 %&mit Biki III' «SILf25)',' KS2l{ 25j; NAB( 25) ' ' 08688*42 

2 SHII; igfLiil DQY < 25J ' ■«*<»*. Kx&m. § 

COMMON /|LOCk4/ FOMM(50,b),SHC (50.21) , 1ST (50) . LT(50), 08693 

2 JT1 (50 , JT2 50), NITfi(50) , iBM(§0) , IBC (50) 08694 
COMMON >3L06k5/ XLS sM, XBS( |A)." FL( 55), AEL \U) , 08695 



2 QZL'( 75) V ' lOVE'L (ftf A " 1 '• J " WA1M '"" y ^ V '°'' 

.COMMON ;BLOCK7/ f( 22), AE( 22), SX( 22), SY( 22), 

2 SS 22 , Qi 22) , QY 22[, gz] 22K Dl] 22JJ 

3 DYJ 22i, az ], 2 2[, ERX( 22), ESY ( 22), ERZ{ 22), 

4 SOU 22), SCY 22f, SOZ 22), 01(221, VI (22), 



/3LOCK5/ XLS( 50), XBS( 50), 

2 SXL( 50), SYL( 50), SZL( 50) ' '* 03696 

COMMON >BLOCK6/ XLLJ 755. XBlJ 75 , QXL ( 75), QYL( 75), 08697 

08698 
08699 
08700 

SOX (22), 22), SQZ( 22); C22)',' ('22)"',' 08702 

1 SiL 22 U, 2*1 22 U V 2I 22)' !2 22 DS 3,3,22), 08703 
6 BH1S( 22), BBiS( 22), TTS( 22), AG{ 22[ 08704**5 

COMKON /BLK1/ TOL, ELE&NT, NJST, ^EEP3C, HCD3C, 08705*79 

2 KEEP2, KEEP3A,KEEP3B,KEEP4A,KEEP4B,KEEP4C,KEEP5A, 08706*61 

3 KEEP5E,KEEP5C,KEEP5D,KEEP6, KEEP7, NCD2, NCD3A, 08707*61 

4 NCJ3B, NCD4A, NCD4B, NCD4C, NCD5A, NCD5E, NCD5C, 08708*61 
3 NCD5D, NCD6, NCD7, IP8, IP9, IP10, ITYPE, 08709*61 

6 IABAN, IFORft, HH. HJT, NST' NLT, M, 08710*61 

7 MP1. 3P2, ISTT, LTT, ITYPEL,IDJ, NSTL 08711*61 
COHHOH /BLK2/ XI,Xfi,X1,X2. H. IH.HSfl, HCU ,X2L,I 1 . 12, NQ 08712 
CCaaOti /BLK3/ HNJT,ENST,MNLT.MNa,HHC5,HNC6,aDJT,MNJS,aNE,aNCS, 08713 

2 HNPCS,aNSS,aNCWM,aN5sT,MNJSS ' * ' 08714*79 

COHBCN /BLK4/ ST1,ST2,ST3,ST4,ST5,ST6 08715 

COHBOB /BLK6/ QT 1 , QT2 , QT3, QI4 , QT5, QT6 08716 

COMMON /3LK7/ INLCPI, IFAE, KCFFJ ,KOFFQB,KOFFSE 08717 

CCfiflON / EI / NL, HI. J1 08718 

COHHON /SKT7/ D1TT(21), V1TT(21), B1TT(21), 08719 

2 02TT|215. V2TT 2lK H2TT(21 08720 

COMMON /SKT14 / IBV (2 1,2, 1&J, FOHOLD (50, 6) , 08721 

2 IRVESE, IIAPE, N3 08722 

IAXOPT = IAXOPS(ISIT) 08723 

[ITYPE . EQ. 1) GO TC 2400 08724 

] IRVRSE ,NE. ) GO TO 2200 08725 

COMMENT - STOfiE HEHEEB-END FORCES OF LAST LOAD STEP FOR STRAIN REVERSAL 08726 

COMMENT - CHECK PURPOSES 08777 

DO 2000 1=1,6 03728 

„„,„ FOMOLD JJ,I = FOBB (JJ,I) 08729 

2000 CONTINUE ' 08730 

COBBEK1 - STORE EXISTING HEKBEH-ENDFOiCES AS MEBBER-ENC-LOADS 0873 1 

QT1 = FOMB(JJ,1) 08732 



311 



QT2 = F0Hfl(JJ,2) 

QT4 = FOMflfJjU 

QT5 = FGHH JJ,5 

QT6 = FOHB (JJ.6' 
GO TO 2400 ' 

CONTINUE 

QT1 = FOBCLO { JJ, 1) 

QX2 = POBOLD ' JJ,2' 

QT3 = FOHC1D i JJ,3 

QT4 = FOHCLD JJ.4' 

QT5 = FOHCLD JJ,5'i 

QT6 = FCfiGLD ( JJ,6 
CONTINUE 

IF (LTT . GT. 0} GO TO 2500 

ZERO LOADS FOfi LOAD TYPE ZSBO * NOTE* FIXEn-FNn-FnjjrF-MAT'PTY 
COHMENT - CALCULATED FOB HESBEE BITH HC LCADS FOB PBESTBESSING OH 
COHHENT - JgHPE|A10HE a EFPECTS AND CASE HHEBE LOADS III BEHAVED 

= oTo 
= o.o 
= o.o 



2200 



2400 
COMHENT 



2450 



2500 



QX(I 

mli 

QZJI 

GO TO 300 

CONTINUE 



COHHENT - SET TEHPOBABY CCNTBCL CONSTANTS FCB LOAI1 T7PT? SBTrn T« 
COBHENT - HAVING ITS JIXED-EHD-FOBCE BATSIX FOBBED 
NCDLT = NCDL(LTT) 
NC61T = NC61 (LTT) 
IF (NCDLT . NE. 0) GO TO 2900 
COMMENT - DISCBETIZE UNIFORM MEBBEB LCADS 
UQXT = OCX (LTT) 
UQYT = UQY(LTT) 
DO 280C 



2800 



QX 

qy 

QZ 
QX 
QY 
QZ 

QX {HP1 

QY (HP1 

QZ (HP1 

QX (HP2 

UY (HP2 

QZ (HE2 
GO TO 3000 
NCSUNIFQBB LCADS 
COBHENT - SU3B00TINE DISCLD DISCBETIZES GENEEAL BEBBEB LOADS QX, QY QZ 

* CALL CONTIN0E ISCLD ( NC61T ' NCDLT ' ZL ' L1 » 
DO FOB EACH ELEMENT 
DO 3400 I = 2.HP1 

IH1 = I - 1 
g??,Jll VALOZS OF ELEHEKT-END-FOBCES STOBED IN ELEEST 
NOW rIIovId D ° NE BY * CA1L TC ELEMF0 HHICH HAS BEEN 



= UQXT*TH 
= UQYT+TH 
= 0.0 

= 0.5*UQXT*Tfl 
= 0.5*UQYT*TH 
= 0.0 

= 0.5*UQIT*TH 

= 0. 5*UQYT*TH 

= 0.0 

= 0.0 

= 0.0 

= 0.0 



COSHEKT 



290 
300. 

ccbbent 



COBHENT 
COMMENT 
COBHENT 



COHBENT 
COHKEST 



D1T 
V1T 
W1T 
U2T 
V2I 
H2T 



U1TT 
yiTT 
S1TT 
U2TT 
V2TT 
H2TT 



START COMPUTATION FOB STATION Ei 
ADJACENT ELEBENT-END-FOBCES AT 



(IHl) = ERX(IH1) + 

(101) = ERY(IB1) + 

(IB1) = EBZ (IH1) + 

(I) = EEX (I) + U2T 

= EEY (I) + V2T 

= EBZ (I + S2T 



lOILIBRIUH EEROES BY ADDING 
STATIONS 



ERX(ial) = ERXJIH1) + D1T 
ERY(lHl) = ERY(IB1) + V1T 
ERZ (IB!) = EBZ (IH1) + S11 

EEX 

EEY 

ERZ 

3400 CONTINUE 

SSS2SSS " COMPLETE CALCULATIONS BY ADDING IN LOADS AND SPRING FOECES 
COBHENT - DO FOR EACH INTEEIOB STATION 
DO 3300 I = 2, B 



IF 
IF 

IF 



(INLOPT ,EQ. 0) SQZ(I) = -SZ(I)*D5 

EiZ(I) = QZ(I) - EBZ (I) + SQZ(I) 

(IAXOpV.EQ. 2) GO TC 3650 ' 



(INLOPT .EQ. Oj SQX(I) = -SX(I)*DX(I) 
ERX(I) = QX(1) - EEX (I) t SOX (I) 

(INLCJ?! .EQ. 0) SQY(I) = -SY(I)iDY(I) 
EBY(I) = QY{1) - EEY (I) ♦ SQY(I) ' 



3650 
COHBENT 
COHHENT 



CALL 



CALL 



GO TO 3800 
CGUTINUE 

TRANSFOfifl SPRING FORCES AND STIFFNESSES IF SPECIFIED IN 
STRUCTURE DIRECTIONS 
SXT = SX{I) 

[hi 



SYT = SY;_, 

SANGLE (SA,SXT,SYT) 
HT 1 1 ■ 
HI (21 
ST (3[ 

KATH31 (SA.HT , FT) 
IF (INLOPT .EQ. Of SQX(I) = -FT(1) 
, r SRXi|} = flit I) - ERk(I) + SQX 



il i IW 



It 



(INLOPT .EQ. 
ERY (I) = QY ' 



0)' SQY(I) - - 
(I) - EEY (I) * S 



FT 



[it* 
it n) 



08733 

08734 

08735 

08736 

08737 

08738 

08739 

08740 

08741 

08742 

08743 

08744 

08745 

08746 

08747 

08748 

08749 

08750 

08751 

08752 

08753 

08754 

08755 

08756 

03757 

08758 

08759 

08760 

08761 

08762 

08763 

08764 

08765 

08766 

08767 

08768 

08769 

08770 

08771 

08772 

08773 

08774 

03775 

08776 

08777 

03778 

03779 

03780 

08781 

08782 

08783 

08784 

08785 

08786 

08787 

08788 

08789 

08790 

08791 

08792 

08793 

08794 

08795 

08796 

08797 

08798 

08799 

08800 

08801 

08802 

08803 

08804 

08805 

08806 

08807 

08808 

08809 

08810 

08811 

08812 

08813 

08814 

08815 

08816 

08817 

08818 

08819 

08820 

08821 

08822 

08823 

08824 

08825 

08826 

08827 

08828 



312 



3800 
COBHENT 



CONTINUE 
00 FOR END 



STATIONS 



IF (INLOPT .EQ. 0) SQZ ( 1) = -ST3*DZ(1) 
•""■'""- MI J1) ♦ SQZ (1) 

,.HPt) = -STb^DZ,. 



IF 



ERZ(1) 
(INLOpV 



IF (IAXOPT 



QZM 

-». 0) S£ 
£SZ(BP1) = QZfHi 



,EQ. 



SQZ(HPt) 

3900 
NLOPT .EC- 0) SQXM) = -ST1*DXM) 
$HU) = QZlt) - fiBi(l) + SQX(i)' 



-EQ. 2) 
IF (INLOPT .EC- 



IF (I 



SQZ(l)- 
ST6*DZ (HP1) 

H) 



IF ( 



IF 



3900 



INLOPT .EQ. 0) SQY(I) = -ST2*Elh) 
EEYH) ~QXlh) - Mri) + SQY(1) ( ' 
INLOPT .EQ. 0) SQX(BPf)' = -ST4*DX(BP1) 

' = QX(Hfl) - EBX(SP1) +SQX(SP1) 
. 0) SQY(BPI) = -ST5*DY7hP1) ' 
= QY HP1) - EBY(HP1) +SQY(BP1) 



.. 01 
ERX(flPl£ = QX(KF1)' 



EBY(BP1) 
GO TO 4100 
CONTINUE 



"S I ISMH8H Eib1^I^S HCES AND STIFF ^ SS ^ IF SPECIFIED IN 



CALL 



CALL 



IF 

IF 



CALL 



CALL 



IF 

IF 



BATH31 (SA,ST,FT) 
INLOPT .EQ. 0/ SQX(1) = -FT(1) 
ESX(1) = QXM) - EEX(1) + SQXM) 
(INLOPT .EQ. 0) SQY(1) = -FT (2) 
EEY(1) = 01(1} - EEY{1) + SQY(1) 
SANGLE ?SA,SI4,SI5) -^ i »') 

«T(2( ■ DYJHP1) 
iiATH31 (SA.BT, 



4100 




CONTINUE 
QT1 
QT2 
QT3 
QT« 
^T5 
2X6 



SQX(BP1) 
SQY(MP1) 



Pi 

BP1 



CGfiflE;iT 
COHMENT 

CALL 
CGBHENT - CALL 

CALL 

9900 



QT1 + EBX 
QT2 + EBY 
QT3 ♦ EBZ 
QT4 + EfiX 
QT5 + EEY(BP1 
„ QI6 + EazJflPI 
CALL GEIP2A FOE SOLUTION 
EQUILIBSIOB EEBORS) 

GEIP2A ( RB,EO,S.SL,L3,L4,L6,5) 

BEHENI j?0fi Ca£ulIt10N OF INCEEBE 1 

HEHENI { S,FOBT,,L6 ) 

CONTINUE 
EETUSN 
END 



OF BEMBEB INCEEBENTAL LOADS (STATION 



TAL FIXED-END-FOBCES 



08829 

08830 

08831 

06832 

08833 

08834 

08835 

08836 

08837 

08838 

08839 

08840 

08841 

08842 

08843 

08844 

08845 

08846 

08847 

06848 

08849 

08850 

08851 

06852 

08853 

08854 

08855 

08856 

08857 

08858 

08859 

08860 

08861 

08862 

08863 

08864 

08865 

08866 

08867 

08868 

06869 

06870 

06871 

06872 

08873 

08874*71 

06875 

08876 

06877 
08878 
06879 



******* 
SU 
COBHENT 
COHHENT 
IB 

cc 

2 

CO 
2 

3 
4 
5 
b 

CO 
2 
3 
4 

5 

f 

CO 
COHHENT 



*************************** SUBBOUTIUE ** 
BROUTINE DISCLD ( NC61T, SCDLT, ZL, LI ) 
- SUBROUTINE DISCLD COHPUIES EQUIviLENT H 



******************** 

EWBEB STATION LOADS 
A BEBBES. 



MHOH /BLOCK6/ ILL (' 75)', 

JjZi(«/2Lt... . iqvEL(75) 



y*i. i id) . luvia. ( /a 
30S /BLOCK7/ F( 22) , 
SZ< 22) , Qtt 25f , 



AE 

QY 
EB 



SX 
QZ 
EE_ 
U1[ 

AG( 



NJI, 
LTT, 



NST, 
ITYPEL, 

Hf TKj, HSC 



102 



CCdilEKT 

1050 
COHKEKT 



COHHENT 

COHHENT 



BafSl 22) , BB2S( 25) , 
SHON /SLS12 TOL, ELEHNl,NjJlt &EEP3C,' 
K2EP2, KEEP3A,KE£P3E, KEEP4A,KE£P4B' 
KESP5fl r KE£P5C # KEEP5D;KEEP6, KEEP7, 
NCD3B, NCD4A, NCD4B, NCD4C. UCD5A. 
NCD5D, NCD6, NCD7, IPS, IF9, 
lABAN^ IFCRK, NH. 
BP1, HP2, ISTT, 
MflON /BLK2/ XL,XE,X1,X2, 
- ZEHO HEBBER LOAD DATA 
DO 1020 I = 1,BP2 
I) =0.0 
I = 0.0 
l[ = 0.0 
_ _2T = NC61T - 1 + UCDLT 
II = NC61T - 1 
II GOES FfiOH NC61T TO NC62T 

II = II + 1 
BEAD DATA FHOB ONE CAED IHAGE (LOADS AT 

Xfl = X5L(Ilj 

QXLT = QXL(II) 

QYLT = QYL II 

QZLT = QZL II 
IF (X5 .HE. 0.0) GO TO 1100 
y A «H BL3 i-OADING SECTION READ ONE CABD 
RIGHT OF SECTION) 

II = II + 1 

XH = X3L(II) 



XEL( 75), QXL( 75), QYL { 75), 
( 22 ) ' 

ITS {22) 



22) , 

22V, 

(22), 



SY( 22) , 

DX| 221, 

EEZ ( 22), 

71 { 22) , 

DS (3,3, 



22, . 

22 ; 

22T 

NCD3C, 

KEEP4C,KEE?5A, 
NCD2, NCD3A, 
NCD5B, NCD5C, 
IP10, HYPE, 
NLT, fi, 
IDJ, NSTL 
,HCU,X2L,I1,I2,NQ 



22) 



QX 

QY 
UZ 
MC 



LEFT OF SECTION) 



IHAGE (LOADS AT 



*********** 

06880 
FOR08881+90 
08882*90 
08883 
08884 
06885 
08886 
08887 
08888 
06889 
, 08890 
08891**5 
08892+79 
08893*61 
08894*61 
08895*61 
08896*61 
08897*61 
08898*61 
08899 
08900 
08901 

08902 

08903 

08904 

08905 

08906 

08907 

08908 

08909 

08910 

08911 

08912 

08913 

08914 

08915 

08916 

08917 

08918 

08919 



313 



noo 



1110 



2100 



COMMENT 
COaaENT 



2150 

2160 

2200 
9000 
9900 



QZL(I 

QXLT 
QYLT 
QZLI 



I! 



. XE) GO TO 2100 

l5^5 N to A ^Sacent S s"ticks NLD T0 disthiedte concentrated 



QXLT, XL, 
QYLT, XL, 
QZLI, XL, 



2.0 



QXET = 

QYBT = 

QZfil = 
GO TO 1110 

QXRT = 

QYBT = 

QZ.ST = 
CONTINUE 
IP ( XL , NE 

comment 

COMMENT 

CALL CONLD 
CALL CONLD 
CALL CONLD 
GO TO 2200 
CONTINUE 

ZI1 = XL/TH + 

11 = ZI1 

X1 = I1*TH - XL - 
ZI2 = XB/TH + 1.0 

12 = ZI2 
X2 = Xfi 
NQ = 12 

DISTRIBUTION 

II TO 12 

IF (QXLT ,EQ 
CALL LIKLD 

IF (QYLT ,BQ 
CALL LIKLD 

IF (QZLT .EQ 
CALL LIKLD 

CONTINUE 

IF (II .LI 

CONTINUE 
RETUBN 
END 



82, 

QY, 
QZ, 



L1 
L1 
11 



IB 



+ TH 



I2*TH 
- 11 
LOADS CALL LINLD TO DISTRIBUTE LOADS STATIONS 

0.0 .AND. QXBT .EC. 0.0) GO TO 2150 

6.0) 

0, 



.AND. QXBT .EQ. 
(QXLT, QXBT, QX, L1 

0.0 .AND. QYBT .EQ. 
(QYLT, QIBf, QY, L1 

0.0 .AND. QZRT .EQ. 
( QZLT, QZfif, QZ, L1 



t) GO TO 2160 



) 



.0) GO TO 2200 



NC62T) GO TO 1050 



81119 

08922 
08923 
08924 
08925 
08926 
08927 
08928 
08929 
08930 
08931 
08932 
08933 
08934 
08935 
08936 
08937 
08938 
08939 
08940 
08941 
08942 
08943 
08944 
08945 
08946 
08947 
08948 
08949 
08950 
08951 
08952 
08953 
08954 
08955 



*****snBRon^Mr^^n**!****^*^* c s SP fi ? 0T f? E ********************************* 
connuV^SIUsSffkAa. dSIs* Sfil'iSfi* tHe L n6^ineab «*«beb solutiono'IIH* 74 

CGBMENT - THIS SOLUTION IS BEQUIBED TC FIND THE SE3EEE-END-FCBCES POR Oflqls 
COHHEOT^Jg JOINT BgDIlIBHl&H CHECK AND FOB THE FINAL^EMBEB^CLUTION 08959 

BEAL*8 JTSHB.JSYES ' ' °§^S t „ 

EEAL*8 MEMBEB 08962 



BEAL*4 DISJT 

DIMENSION EK(L6,L4), RO (L6) , WJL6) 
DIMENSION BCJ3.3) ,' DBM (i) , ' SA (3,3 , 
DIMENSION 180(4, 4[,DHS4(4f nlJ ' J '' 
DIMENSION ALPflV<4lf 
X(2i 



DMS(3) , FHM(6) , FMT(3) 



COMMON /BLOCK1/ 



QZZ (25) , six (25), 

DYY 251, DZZ|25|' 

EBXi(25f, EBYY(25f, 

N3XXJ25), NSYYJ25K 

NSYP(25J. ISTJS(25f 

COMMON /BALAQ1/ QVV(25), 

2 HVV (25) , NSVV(25f 

"ION /BLOCK2/ DXS( 25), 

DC2S ( 25) , PEF( 25C 

PRAG(25), ELE8S(25[, 

IOPOPf 25), IPINL( 25) , 

NAL ( 25) , NSXLf 25) , 



J I; 

•IS: 



co a HON , 

2 DC2S ( 

3 PHAG( 

4 
5 



BXX 

EHZ_ 
NSZZ 

SVV(25) , 

DYS( 25). 
PRAE( 25), 

IPINR( 25) , 




D¥V(25) , 

ZLS ( 25) , 
23( V 25), 



NC5 1 , 

NSZLl 



25 
25 



QYY(25) , 
DXX (25) , 
RZZ(25) , 
SHJ (25)., 
NSXP(25) , 

EE7V(25) , 

DC1S( 25) , 
«H( 25),' 

INLOP ( 25) , 
NAB/ 25) , 
XOP5 ( 25) 



6 Ssxi(25/, sixi] is ; sip mi ; mi Ml ]• mhiytex 

2 CCt1M ^ K /3ALA0i/ JST(i^ ,ysS(25):HLJ , (25) r HE J {25)ULJ(25)fvUJ(25), 
coaaoE Ahociz/ DXt/( 25), DYL( 25), ZLL( 25). .«-t». *<=. 
fcl\[ll\' Wl]ii ° al|25}; aCDLVIsf, 

50), 



DC1L( 25). 
IAXCPL( 25) , 



jT2( io) ; ; 



NITM(5t) 
XRS( 50) , 
SZL( 50 
XEL ( 75 



hi 1 ; 



0) 
5), 

:( 22) , 

Mm 



IB! 
FL( 

QXL( 75) , 



LI (50), 

iafc( 





2 JT1 (50) , j-±t 

CCHHCN /BL0CS5/ XLS 
2 SXL( 50) , 5YL 50 

CCSiSON /BLOCK6/ XLL ( 75),' 
2 QZL( 75) , IOVfiL(75j 

CCaauN /3LOCK7/ F( 22), 

2 SZ( 221 , QX( 22f , 

3 DY 22J, DZ ( 22[' 

4 SQX( 22) , SOY{ 22/ , 

5 HTf l 22)'' U2( l 22):' 

6 BK1S( 22) . BH2S( 22) , 

coaaoK /BLOC12/ sm (20,10), 

2 YI(20,10), HSSf20,ltr, 

COM.10N /BLOC13/ NPTS( 8), 
2 NSIT(II). NEPTJ11) 

COMMON /BLOC21/ ACCJTMDO t , 
2 OVELJT(100) ,FACCJf(10&f ,FDAHJT( 

COMMON /BLK1/ TOL, ELEHNl, NJST, fttjSi-jJj, NUUJC, 

2 KEEP2, KEEP3A,KE£P3E,KEEP4A,KEEP4E,KEEP4C,KEEP5A, 

3 KE2P5E,KEEP5C,KLEP5D, KEEP6, KESP7, NCD2, NCD3A, 
I ?S81S* NCD4A, SCD4B, NCD4C, HCD5A, NCD5B, HCD5c' 

5 ??g 50 ' NCDt, t NC D ? » IPS, IP9, IP10, ITY°E. 

6 IABAS, IFOR*, m t NJT, NST, NLT, H, 



-,50) 
AELj 50) , 



AEI 
QY| 
ERX. 

TTS 
EH. 

NA itu) t 
ISS ( 8) , 

7ELJT(100) .ZMASSB (100) ,DACCJT ( 1001 , 

100) ,CDASEM106) ,DISJT(80,71 

KEEP3C,NCD3C, 



VI ('22) , 
DS(3,3, 22), 

DI(20.10) . 
NCtfAf20). IRECT(20,10) 
N3IG 08,11) ,NEPS(08,11 , 



08963 

08964*74 

08965 

08966*75 

08967 

08968 

08969 

08970 

08971 

08972 

08973 

08974*70 

08975*75 

08976*42 

08977*42 

08978*42 

08979*42 

08980*42 

08981*42 

08982*79 

08983*80 

08984 

08985 

08986 

08987 

08988 

08989 

08990 

08991 

08992 

08993 

08994 

08995 

08996 

08997 

08998**5 

08999 

09000 

09001 

09002 

09003*65 

09004*88 

09005*79 

09006*61 

09007*61 

09008*61 

09009*61 

09010*61 



314 



'cGMMON Alii/ lg!h.xljf3?' LTT ' H5?I*IifiJ&fi,X2f?I*,I2,»Q 

common /blk4/ sn ,st2,si3,st4,st5,st6 

COMMON /BLK5/ NFSOB.Nf TF, 5 1 ,n3 
COMMON /BLKb/ QT1 , 0T2 .0.TJ , C14, QT5, QT6 
COMBOS ^iV if 6 Sl'jf '* OF "' KO "Q"^OF]? S E 
2 C0HB0B/IIC/ E||^B8|5 j E8UBB2»OTI,ClI,OTI,HH(20),flJ(20),HHITP, 

COMMON /NIT/ APEOB ' 

COSMON /SKT2/ 
2 8BV(25, 10), 

4 WBTYP(25,1D) 

COflBOH /SKT5/ 



HBX(25.10) 

ftBXP " 
KfiTZ 



25,10 , BBI(25, 10), WBZ(25,10), 
25,105, WHYP(25,1&f, «BTX(25.1of, 
25,10), HBTV 25^0 , iBTXl? (25, 10) , 



COMMON /SKT6/ 
COMMON /SKI9/ 
COMMON /SKT10/ 
COMMON /SKT11/ 
CGMMOK /SKT13/ 



HEXM (21,10), SEYM (21,10), SBZ3 (21,10) 



nxi ri.cn idui , 

ENDFOfifSO.S) 

NDIV (20,10), NPCTOT(20) 

KSSINL. MSSIB1 

EPfi1S(21,10,3l,EPHT1S(21,10,3) , 

"common /skt14 / iRrWAlVof] ^ '"" 2s[ "' % °4n 

2 IBVBSE, IIAPE, S3 

COMMON /SKT15/ JJ 
COMMON /SXT17/ N4 
COMMON /SKT18/ NCHECK 

COMMON /SKT20/ MCBGON (2 1 ,3) , MCUBEV(21,3) 
CCMflOD /SKT22/ TIME, JT, IBDYN, IfiSflif?T) 



MOLD(50,6) , 



LOflflUU /SKXIZ/ TIME, JT, IBC 

COMMON /3KT27/ IEEAD, IfiEITE 

COMMON /3KT30/ MSTIF"" 

COMMON /SKT32/ EPBF1 



COMMON /3KT30/ MSTIF(25), KLOAD(25), MODEL (25) 

EPBFT1f21,10,3] 



21,10,3) 

SLBFT1 (21,10,3) 

SLBF2 (21,10,3 

EPSMAX i 21,2, 10) 

YGROK (21,2,10) 



COMMON /CHAN1/ JTSHE 

DATA PRINT /4HBINT/ 



EPBF2 (21,10,3) 
SLBFT2i 21,10,3) 
EPSMIN 21,2,10) 
ITGBOM(21,2,10) 



SIBF1 (21,10,3), 
EPBFT2(21,10,3) , 

EPSPBE(21,2,10) , 



IA.X, 

15H 



40 FORMAT 
45 FCEMAT 
5 1 FORMAT 
2 



-3 15H 

32 FORMAT (88X.6H 

53 FORMAT (//,11B 
2 15,//) 

54 FORMAT ( 
2 

55 FORMAT ( 



uiiA A.a.u /ia ,ih», 

DATA MEMBEE /4HMEEB/ 

DATA SHEAfi /5HSHEAB/ 

DATA JSYES /5HJSYES/ 
89X,3(5HIXXXX) ,1HI,//) 
, 17X, 6 (1PE11.3) ,'it, 41A1 ) 
/, 5X,2I5, /,15H FBOM JOINT ,2X,6E1 1, 



CENTEBI.INE»2X,6E11.3,/', 



3,/, 



RATION, 



COMMENT 

C 

C 

C 

COMMENT 



- IB DIN = 



46H 
24H 
44H 
33H 
1 



IF 



2000 



C02SBHT 



EXEC0TED NO 
ACCESSED A 
(BACKED UP) 
IF ( IHPE 
SET TEKPORA 
ISTT 
LTT 
( ISTT 
M = MS 
MP1= M+ 
MP2= B+ 
MP22 = 
IAXOPT 
IPINLT 
IPINE-I 
ZL = Z 
NCDS1 
NC51T 
1NLOPT 
MODELI 
ELEMNT 
TH = Z 
H = 0. 
HSQ = 
HCU = 
NL = 3 
ML = 1 
NFSUE 
INLOET 
NHINGE 
(ELEMNT 
NALT 
NCDAT 
NW3ITE 
CONTINUE 
IF (ELEMNT 
IF (INLGPT 
IF (NCDST , 
NONPBISMATI 



HEaB iStlI<; 2 S§ converge d 3 afteb itebatioh.is) 

MEMBER, 15, 30H NOT CONVERGED AFTEB ITE 

mcSoiSFiiiSiS! SPSS, Q_ij CDBVE EXCEEDED 0N - 

EXCEE5E^O^ T pR IcE fl |g!i S lII!If!o H P AINCOBVE ' 
u u„5 £ ??21?„£ H £ T TaE PARTICULAR TIME STEP BEING 
W HAS ALREADY BEEN COHPLETLY SOLVED ONCE BUT Ts 
GAIN THIS TIME ONLY FOB THE P0EPOSE OF ' S 

STIFFNESS FOBMATICN AND MEMBEE-END-FOBCES COMPUTE 
«-L£« £. I LHDlH — U 
BY CCNTBCL CONSTANTS 

1ST (J J) 
LT(JJ) 

EC. ) GO TC 9900 
TIF (ISTT) 

2 

MP2/2 

= lAXOPS(ISTT) 

= IPINL(ISTT) 

= IPINfi(ISIT) 
LS (ISTT1 
= NCDS (ISTT) 
= NC51(ISTT) 

= INLOP(ISTT) 

= MODEL (ISTT) 

= ELEMN ISTT) 
L/M 
5*TH 
H*H 
HSQ*H 
*MP1 



IF ( 



I? 



= 22 

.Eg- ) GO TO 2000 

= / 
. EQ. SHEAB) NHINGE=1 

= NAL(ISTI) 

= NCDA(ISTT) 
B = NSXL(lSTl)+NSYL(ISTT) +NSZL(ISTT) 



• EQ- SHEAR) GO TC 23010 

-EQ- 1) GO TC 25C0 

20.. 0) GO TC 2100 

C MEMBER DISCBETIZE MEMBER STIFFNESS DATA 



09011*61 

09012 

09013 

09014*79 

09015 

09016 

09017 

09018 

09019 

09020*88 

09021*88 

09022 

09023*84 

09024*84 

09025*84 

09026*84 

09027 

09028 

09029 

09030 

09031 

09032 

09033 

09034 

09035 

09036 

09037 

09038 

09039 

09040 

09041 

09042 

09043 

09044 

09045 

09046 

09047 

09048 

09049*75 

09050 

09051 

09052*11 

09053*16 

09054*75 

09055 

09056 

09057 

09058 

09059 

09060 

09061 

09062 

09063 

09064 

09065 

09066 

09067 

09068 

09069 

09070 

09071 

09072 

09073 

09074 

09075 

09076 

09077 

09078 

09079 

09080 

09081 

09082 

09083 

09084 

09085 

09086 

09087 

09088*10 
09089 

09090 

09091 

09092 

09093 

09094 

09095 

09096 

09097*78 

09098*78 

09099 

09100 

09101 

09102 

09103*10 

09104 

09105 

09106 



315 



CALL G0 TO 2^§ CS1 <«"1T, N CDST,ZL,L1) o§107 

2100 CONTINUE 0|J08 

COMMENT - PSISHATIC MEMBEE DISCB E1IZE MEBBEB STIFFNESS DATA Bll 10 

PSAEI = PbIe(ISTT) nqiio 

DO 2300 I = 1,kp2 nlUl 

SY(I = 0.0 9|1^ 

SZjlJ = 0.0 nllU 

SQi.ll) = 0.0 SgJJ§ 



i: 



DC (3,1) =0.0 




09118 



SQZJI = 0.0 0Q11O 

Ai(M52) =0.0 SS]23 

GO TO F ii P 2) = °-° Sll 1 !^ 

gg^ljj? I |§lff A S5g E £ £HBEB MSCEET "2 MEBBEB STIFFNESS DATA FOE A HMVAl 

23010 CONTINUE S!, 12 §!^ 

IP (INLOPI .10, 1) GO TC 2500 olllojfif 

PBFT = PEF(ISTT) oqitilul 

PEAET = PBAE(ISTT) noiloiin 

PBAGT = PfiAGflSTT} nQiT 2 I!n 

DO 23030 I = 1,flpi ' oliittJin 

SX [ 1 } = °'° 09l3s*in 

SI I = 0.0 nqi3I!18 

SZJij =0.0 09137*10 

SQXfi) = 0.0 nqiiflJin 

SQYjlj = 0.0 09139*10 

Mi : ¥h mn:n 

Ae}«P27 2*0 09146*10 

FfMP2) } = 09147*10 

MfflPSl = 6 09148*10 

2400 CONTINUE 2) °*° R!l^* 10 

COMHENT - STOBE UBEEB - END - BESTBAINTS (LI1IEAE SPEINGS) 09151 

It? = II 1 si Si 



SM-HW §11I 3 4 

Si = HW1 81111 

ST6 = SZ(HP1) naiCT 

2500 CONTINUE l ' SS " 

IF ] IiDYN .EQ. 1 ) GO TO 2700 09159 

IF (NITM(JJ) .EC. BNIIfl + 1) GO TO 2700 naitn 

COdBENl - SKIP FOE'fliiAL REKBEB SOLUTION 09 fil 

COMMENT - SET OP MEH3EBS IB ANSFOBBATICN BATBI2 DC 09162 

g 3:11 ' l:°o Mill 



09164 



DC 3' 2 - 0*0 09165 

DC{1,1| = DCISflSTT) OqifiS 

DC (1,2) = DC2S?ISTT5 gqif q 

DC 2,1 = -DCjl.2) 09170 

DC i 2 ' 2 = DC(T,1) 8II4S 

270U CONTINUE Sqitt 

IF (LTT .BE. ) GO TO 2750 00173 

COMMENT - ZE30HEHBEP. LOADS FOB LCAD TIPS ZEBO 09174 

DO 2720 I — 1 # MP 2 rtniTc 

QXm = 0.0 09176 

QI I = 0.0 0917? 

" 72 ° GO TO Q liSo = °*° "ItI 

C 3*JW" ~ ?ohi°/u¥ CL C0HS ™ S E| If 

NCDL1 = NCDL(LTT) oqiR? 

BC6 1T = NC61 LTT( oqia* 

IF (NCDLT .HE. 0) GO TO 2900 nqina 

COMMENT - UNIFOBBLY LOADED BEaBEE DISCEETIZE KEMBEE LOADS 09185 

fflS.:jppHi ifw 

= U52T*TB oil 8# 

2800 2Z(l5 = 0.0 Qq 1 1? 

0.5*UQXT*TH 09192 

0.|*U5lT*TB 09193 

='0. 5*UQXT*TH 09195 

I 0.5*0ail»TH §1111 

" X- X 09197 

u. u no 1 qq 



09198 
09199 
09200 

COMMENT - DI3CRETIZE GENEEAL MEHBEE LOADS 0970? 



8*2 09199 

u>u 09200 



09202 



316 



290C C 

3000 
COMMENT 



COBHEST 



3050 



3052 



3054 
3055 



3056 



3058 
30551 



30561 



3058 1 
3059 



3060 
3065 



ALL CONTINUE ISCLD ( NC61T ' SCDLT ' ZL ' i1 > 
STORE MEMBEE-EKD-LOADS 011 -056 
fill ■ QXM) 
QT2 = QYh) 
QT3 = QZ(l[ 
QT4 = QX(HP1) 
QT5 = QI/MP1J 
QI6 = QZiMPl) 
NITEEd (JJ) i 1 
HYPE .SB. 3 ) SO 10 3076 
NITF .GT. 1) GO TC 3080 
ITYPE.EC.2)GO TO 3080 
FOB FISAL_HEBBEB SOLUTION 

NITB + 1) GO TO 3080 



IF (NITB{JJ) .EQ- MI 
DO 3050 I = l,gp2 
DX<I) =0.0 
DY(l{ =0.0 
DZil] = 0.0 



I INLOPT .EQ. ) 
1 NWBITE .EC- ) 
3052 I = 2,HP1 ' 



IF 

IF 

DO _ 

DO 3052 J = 1!10 

HHXH {I, J 

HfiTXfl I, J 

SBYM 

WBTYB 

WBZM 

HBTZH 
CONTINUE 
DO 3054 I = 2,BP1 
DO 3054 N = 1,3 

BCUREV(I,N) 
CONTINUE 
CONTINUE 
IF ( HODELT .LE 



GO TO 3100 

GO TO 3055 



0.0 
0.0 
0.0 
0.0 

0.0 
0.0 



30 



IF iELESNT .EC. SHEA 

DO 3056 I = 2,HP1 

DO 3056 J = 1,BNPCS 

DO 3056 S = 1,BSSIB1 

EPB1S (I,J,K) = 

EPKT13(I,J,K) = 

EPH2S (I,J,K) = 

EPEI2S(I,J,K) = 

CONTINUE 

IF ? HODELT 

DO 3058 I = 

DO 3053 J = 



k 



GC TO 3100 
GO TO 3055 1 



0-0 

CO 
0.0 
0.0 



.EQ. ) GO TO 3071 

2,HP1 

1.HNPCS 



1,BSSIH1 



= 0. 
= 0, 
= 0. 



0.0 
0.0 
0.0 
0.0 
0.0 



DO 3058 K = 

EPBF1 , 

SPBFT1 (l,J,K 

SLBF1 (I,J,K 

SLBFT1 (I,J,Ki 

EPBF2 |l,J,K'i 

EPBFT2 (I,J,K 

SLBF2 (I,J,K 

SLBFT2(I,J,K' I 
CONTINUE 
GO TO 3059 
CONTINUE 
DO 3056 1 I 
DO 3056 1 J 
DO 30561 K 

EPR1S 

EPBI1S 
CONTINUE 
IF ( MODEL! .EQ. ) GO TO 3071 
DO 30581 I = 2,BP1 
DO 3058 1 J = 1,MNPCS 
DO 30581 K = 1-BSSIH1 



2,MP1 
= 1,HNPCS 
= 1.BSSIH1 
(1,0, K) = 0.0 
; I,J,K) =0.0 



EPBF1 (1,5, K 
EPBFT1 (I, J,K 
SLBF1 (I,J,K 
SLBFT1 (I#J#K 

CONTINUE 

CONTINUE 

DO 3070 I = 2,MP1 

DO 3070 L = 1.NHINGE 
ICUMD = 



0.0 
0.0 
0.0 
0.0 



DO 3065 J = 
NSSLI 
NDIV1 
SIGHA 
P5LCN 



1,NCDAT 

= NSS (NAL1,J) 
= NDIV(NALT.j( 
= NSIG(NSSLT,2) 
= NE?S(NSSLT,2j 



DO 3060 IDVT = 1.NDIVT 

ICUMD = ICUBU + 1 



* SB(NALT,J) 

* EB(NA1T,J) 



EPSSAX (I, L, ICUBU 



IF 



PSLCN 



EPSMIN I,L,ICUMU = -PSLCN 
EPSPBE (I,L,ICUMO = 0.0 
( rtODELT .BE. 2 ) GG TC 3060 
YGBOW (I, L, ICUBU) = SIGMA 
YTGKCi* (I, L, ICUBU) = SIGMA 



CONTINUE 
CONTINUE 

IF ( ICUMU ,GE. MNPCS ) 
I3EGIN = ICUMU + 1 



GC TC 3070 



09204 

09205 

09206 

09207 

09208 

09209 

09210 

09211 

09212 

09213 

09214 

09215 

09216 

09217 

09218 

09219 

09220 

09221 

09222 

09223 

09224 

09225 

09226 

09227 

09228 

09229 

09230 

09231 

09232 

09233 

09234 

09235 

09236 

09237 

09238 

09239*78 

09240 

09241 

09242 

09243 

09244 

09245 

09246 

09247 

09248 

09249 

09250 

09251 

09252 

09253 

09254 

09255 

09256 

09257 

09258 

09259 

09260 

09261*78 

09262*78 

09263*78 

09264*78 

09265*78 

09266*78 

09267*78 

09268*78 

09269*78 

09270*78 

09271*78 

09272*78 

09273*78 

09274*78 

09275*78 

09276*78 

09277*78 

09278*78 

09279 

09280*78 

09281 

09282 

09283 

09284 

09285 

09286 

09287 

09288 

09289 

09290 

09291 

09292 

09293 

09294 

09295 

09296 

09297 

09298 



317 



DO 3067 ICUMU = IBEGIN, MNPCS 09?qq 

EPSBAXfl.L.ICUBU, = PSLCN 09300 

EPSMIN I, L.ICUHU = -PSLON 09301 

td EPSPBE (I. L.ICUHU) = 0.0 09302 

IF { MODELT .HE. 2 ) 5Q TO 3067 0930 3 

YGHOW (X,l,XC8feu) = SIGMA 09304 

3067 C OT TlS! ,0,k ' , -' IC ™ = SIGMA lljii 

DO 3072 I = 2.MF1 oqqnq 

DO 3072 L = 1.NHINGE 09310*78 

DO 3072 J = i'hKPCS 09311 

IBV(I,L,J) = nqii? 

3072 CONTINUE nl*i* 

GO TO 3 100 nq^ln 

3076 COHTINUE S||2S 

£ 5I„ A «8IIifiiS SOLUTION FAILS AND &FTERIABDS HEHSCL IS ACCESSED 09316+90 

C FOB PURPOSES OF PRINTING MEHBEB BESULTS AT THE END OF THE LAST09317 

C STORED TIHE STEP, THEN VALUES MUST BE READ OFF OHIT'IREAD' 09318 

C NOTE:- (LOOK FOR COMMENTS IN SUBROUTINE PBINT9 DESCRIBING AT WAT 09319 

£ i§?H V £ LS * VALUES ARE WRITTEN CH THE PERMANENT UNIT . ) 09320 

C HEUCE THE FOLLOWING STATEMENTS DPTO BEFCBE STMNT 30801 09321 

_. IF ( IABAN .EQ. ) GO TO 3080 09177 

HEAD I IBEAD ) ( DI(I)„ DI(I). DZ (I) , 1=1, HP2 ) 09323 

If ( INLOPT l .EQ. b'\ Gd T6 3300* ' 09324 

„ IF ( NHRI1E .EQ. J GO TO 3078 09325 

READ (IREAD ) 7j [WSXB( I. J) , HRTXH (I, J) , SJRYH II. J) .WBTIM (I, J) , 09326 

3078 2 CONTINUE « B « "'^ ** W.5) . .1=1, Iflf .' i-2,BP tf ' ' g|||| 

IF ( MODELT .LE. -1 » GO TO 3300 09379 

»..„ X ?,j!JrS a,,S * E 2- SHEAR) GO TO 3079 09330*81 

READ IXiZkO j (((EPR1SiI,J,8) .EERT1 S(I , J, K) ,EPB2S (I, J, K) . 09331 

READ (IREAD) CC(||||tr|^ K> 1|ifi tCX a Kj i"|l 2 JX,a K^ 0933 

3079 CONTINUE nllllJSl 

READ (IREAD) ( { (SPB1 S (I, J , K) ,EERT1 S (I , J,K) , 09340*81 

2 r. , „™^J = 1r«S S * H '>' J = 1c«»PCS); 1=2, MP1 ) 09341*81 

IF ( MODELT .EQ. ) GO TO 3300 09342*8 

READ (IREAD ) ( ( (EPB F1 (I, J K) , EPBFT1 (I, J ,K) , SLBF1 (I,J,K). 09343*81 

3C791 2 CONTINUE SLBFT 1 fl , J, K f , K=1,MSSI«1 ) ,5= 1 , MNPCS) , I= 2 ', &P1) §9344*81 

READ (IREAD ) ( ( (EPSHAX (I, L, J) , EPSMIN (I ,L, J) , EPSPBE (I.L.J) , 09346 

2 IF t 40DELT .NE. = ]'re S TO'3^00 1 ' NBI8GE >' * " 2»»1 ) 81J3Z* 81 

READ (I2EAD ) (((YGBOH £1.1. J) , YTGHOH (I^L , J) , J = 1, MNPCS ), 09349 

2 m m non L = 1 '»™ E f, I = 2;HP1 )" 09350*81 

uO 10 JjUO 0Q151 

30«0 CONTINUE 09357 

READ (N1) j DX(I), DY(I), DZ(I), I = 1,MP2 ) 09353 

IF ( INLOET .EC. ) GO TO 3l66 ' 09354 



IF ( INLOET .EC. ) GO TO 3100 ' 

IF ( NWRIIE .EQ. J GO TO 3085 
|EAD (H1j ( ( MfiXMfl.j), HBTXM(I.J), JiRYM(I,J), 
IU2EU.J . iRTZM I,J), 5=1,10), I=2,MP1 ) 



09354 
09355 
09356 
09357 



IF | MODELT .LE. -1 ) GC TO 3100 09361 

IF {ELSMNT .EQ. SHEAR) GO TO 3086 09362*78 

KEAD (St) ( ( EJ|TSjI f J,K , £P5T1S(I,J,K) , EPB2S (I , J, K) , 09363 

tPRT2s{l,J,Kj , K = I.MsSlMlJ, J= 1 , MNPCS J , i=2, MP 1 ) 09364 



2W2/?rT ( 7i 1J ia4yS^T 8 l?* J Ui fi ffif ll{ l'? , l,W , t I » a >» »2IYM(I,J), 09356 

^WiiiulI.J), »RIZM (I, J) , J=1,10), 1=2, MP1 ) 09357 

IF SrifllJJ) .EQ. MNI1K+V) GO TO 3085 09358 

3085 VJ^kll ! I (I '! J : !: 1 :! j :.': 2,!,p1 ' HJI! 

IF ( MODELtTeQ.^'o')"' GC TO 3090 

READ (N1 ) (((EPBF1 (I,J, K), EPBFT1 fl , J ,K) , SLB F1 (I,J,K), 09366 

i SLBFT1 I,J,K , EPBF2 Jl,J,K K EPBFT2JI.J K ', 09367 

3 SLBF2 (l.J.K , SLBFT2JI.J.K , K=1,KsilM1 ), 09368 

4 m ,n „ la « J = !#«"« ), I = 2,flpf f 09369 

GO TO 3088 0P370*7S 

3060 CONTINUE 09371*78 

READ (N1) ((( EPfi1S(I t J,K) , EPRT 1S (I, J.K) , 09372*78 

2 K = I.MSSlMI), J=1.MNPCS); 1=2, MP1 ) 09373*78 

IF { MODELT .EQ. ) GC TO 5090 09374*78 

READ (HI ) {((EPBF1 (I,J,K) , EPBFT1 (I,J,K) , SLBF1 (I,J,K), 09375*78 

3088 2 CONTINUE SLBFT1 {l , ^ kJ ,K=1 ,HSSIM 1 ,,5=1, MNPCS ,,I=2 ; ,&P1 ) 09376*78 

READ (HI ) (((EPSt!AX(I,L.J>, EPSMIN (I.L.J) , EPSPBE (I,L, J), 09378 

2 J= 1, MNPCS ), L = 1,NHINGE ), I ■ 2,flP1 ) 09379*78 

IF ( MODELT .ME. 2 ) GO TO 5o90 ' 09380 

RaAD (N1 ) (((YGROH (I.L.J), YTGROW (I,L, J) , J = 1, MNPCS ), 09381 

3090 2 CONTINUE L = ' ' ^^ f ' X = 2 '^ 1 > °^ 8 8 3 2 * 78 

?! gjsas^tif'ii "psrio* 3f8o to 330 ° mn 

, inft K2AD iNJ) (( (IR7(I,L,J),J=1,HNPCS) ,L = 1 ,NHINGE) , 1=2 , HP1) 09386*78 

IF ( IRDYN .EQ. 1 ) GO TO 3500 09388 

IF (NITK(JJ) .EQ. aUITK + 1) GC TC 3300 09389 

COMMENT - SKI? FOR FISAL KEMBER SOLUTION 09390 

COMMENT - SET MES3ER-EKD-DISPLACEKENTS IN STRUCTURE COORDINATES DMS 09391 

LOMMENT - EQUAL TO STRUCTURE JOINT DISPLACEMENTS AT FECM JOINT 09392 

J1 I = JT1 (JJ) 09393 

IF (JTSHE . NE. JSYES) GC TO 3110 09394*75 



318 



IF (JSTfJII) -EC. 0) GC TO 3110 
IF (DABS (EC IS (1ST T)) . GT. 0.99) 
IF (DABS(BC1S (ISTT) ) .IE. 0.99) 



KEY=1 
, KEI=3 
CALL TENSFB (KEY, J1I,TRD, 3, 4) 

DBS4(1) = DXX(J1I) 
DMS4 12) = DYY(J1l'i 
DBS4(3J = DZZ(J1Ii 
DflS4(4) = DVV(J1I 
CALL aULT (TED, DBS4, DBS, 3,4,1) 

GO TO 3115 
3110 CONTINUE 

Das (1) = DXX (J1I) 
DHS (2) « DYY (J1I) 
.... DHS (3) = DZZ(J1I) 

3115 CONTINUE 

COBBENT - TRANSFOBB DHS TC DHH AT FROM JOINT 

CALL HATH31 (DC , DBS, DHH) 

COaaENI - SET HEHBER END-LOADS TO 1.0240 TIHES DBH AT FBCB JOINT 
ERX(l) = (DHH(I) - DX(1))*1.0E20 
IF (EABS(EBX(1)).LT.1.0E07) EBXf1)=" 

ERY(l) = (DHBJ21 - DY(1)J*t. 6l 
IF (DA3S (EBY(1)). " 
IF (IPINLT .EQ. 1) GO TO 3120 
. . ERZ(1) -. (DHHT 

GO 
3120 ERZ(1) = 0.0 

3150 CONTINUE 

COMaENT - EEPEAT ABOVE FCE TO JOINT 
J2I = JT2(JJ) 
JTSHR .HE. JSYES) GC TO 3160 
JST(J2I) .EQ. 0) GO TO 3160 
DABS (EC1S (ISTT)) . GT. 0.99) 
.DABSJEC1S ISTT)). . LE. 0.99 
CALL TRNSF3 (KEY , J2I .TED. 3,4 

= DXX(J2I) 
= DYY (J2I 



.inaj2) - dy(1); H. 0E20 

'1)).LT\1.0E07) EEY(1)=0.0 
. iQ. 1) GO TO 3120 
ERZM) = (DHMj[3) - DZ(1))*1.0E20 
:F (DABSjE3Z(1)).LT.l.0E07) EBZ(1)=0.0 

;o to 3150 



DBS4 (1) 
DBS4 (2) 
DBS4 (3) 
DBS 4 (4) 
HOLT 



CALL 

GO TO 3165 
31o0 CONTINUE 

DBS (1 
DBS 12 
DHS (3 
3165 CONTINUE 

CALL HATH31 

EEX (HP1) 



= DZZ (J2I 

= DVV(J2I 
(TED,DBS4, 



KEY=2 
KEY=4 



BS, 3, 4,1) 



DXX (J2I 

DYY (J2I 
DZZ J2I 



(DC.DES.EHB) 
= (DHB(l) - DX(HP1) ) +1.0E20 



IF 



IF 
IF 



(DABS (ERX(HP1) ) 
ERY(BP1) = (D 

(DABSjERYjf 

l *PINET .2 
ERZ(HP1) = ( 



IT. 1.0E07) 



ERY(flP1) = (DBfl{2) - DY (BP 1) ) * 1. OE20 
3ABSJERYVaP1) V ) ,IT.1.0E07f EBy'(MP 
IPINfiT .EQ. 1 GO TC 3220 



ERX (HP1i=0.0 
•'1.DE20 
P1) = 0.0 



,_HB(3) - DZ(BPI) )*1. 
IF JDABSjEfiZ(HPI) J.LT.1.0E07) " 



3220 
3250 
3300 
3500 
COBBENT 

cohheni 

COMSBl 

COBBENT 

C 

c 

C 



36001 



3501 
COKSEBT 
C 

C 

C 

C0 3MENT 

COBBENT 

CGSKKBI - 

COBBENT 
COBBENT 
COQEENT 
COBBENT 

3502 
COBBENT 



GO 



0E20 

*0"323B EEZ(flPi) = o.o 

EEZ(»P1) =0.0 

CONTINUE 

CONTINUE 

CONTINUE 

Sx^S T .J^I A i i y E SOIOTICN FOB MEHBER DISPLACEMENTS CONSISTENT 

WITH APPLIED LOADS AND IBPOSED DISPLACEBENTS F2CB FBABE 

SO Lai] TXO N 

IF ( INLOPT .EQ. ) GO TO 3505 

THE FOLLOWING STATEBENTS ( UPTO # 3501 ) DETEEBINS THE 
PROPER VALUE FOE INDEX . 

INDEX = UB IS NOT SET EQUAL TO UET 
IS SET EQUAL TO UET 







INDEX = 1 

INDEX 
IF ( NITHfJJ 
IF ( ITYPE 
IF I IRDYti .EQ. 
CONTINUE 



US 



^: E §- 



i 



HNITB+1 
GO TO 3 
GO TC 



) GO 
5001 
3501 



TO 3501 



IF 

IF 

IF 

CON 

THE 



, AND. 
) GO 

.AND. 



NITEEK(JJ) 
TO 3501 



EQ. 2 ) INDEX = 1 



NITEEB(JJ) .EQ. 2 ) INDEX = 1 
UPTO * 3504 ) DETEEBINE THE 



NOT 



DONE 
DONE 



NITF .EQ. 
ITYPE .GE 
ITAPE .EQ 
INUE 

FOLLOWING STATEBENTS ( 
PBOPEH VALUE FOR NCHECK 
NCHECK = EEVEESAL CHECK IS 
NCHECK = 1 EEVEESAL CHECK IS 

NCHECK = 

REVEBSAL CHECK BUST NOT BE DONE HHILE TABLE 9 IS BEING 
IF ( NITB(JJ) .EQ. HNITB+1 ) GC TO 3504 
FOB NITF = 1 ONLY STRAIN EEVEESAL CHECK DONE. 
IF ( NITF .GT. 1 ) GO TO 3504 
IF ( ITYPE .IE. 2 ) GO TO 3502 
EEVEESAL CHECK NOT NEEDED IN FIRST TIBE STEP 
EQ. 1 I GO TO 3504 
ANALYSIS, EEVEESAL CHECK 



09395*75 

09396*75 

09397*75 

09398*75 

09399*75 

09400*75 

09401*75 

09402*75 

09403*75 

09404*75 

09405*75 

09406 

09407 

09408 

09409*75 

09410 

09411 

09412 

09413 

09414 

09415 

09416 

09417 

09418 

09419 

09420 

09421 

09422 

09423 

09424 

09425*75 

09426*75 

09427*75 

09428*75 

09429*75 

09430*75 

09431*75 

09432*75 

09433*75 

09434*75 

09435*75 

09436*75 

09437 

09438 

09439 

09440*75 

09441*75 

09442 



7 JT 

THE DYNAHIC 



IF 

IN 

THE PARTICULAR 

INSTANT. IT IS 



IS 



j.->, m.ui^/u, v-ncv,rv u NEEDED ONLY WHEN 
TIBS STEP IS BEING EXECUTED FOR THE FIBST 
NOT APPLICABLE WHEN A PABTICULAB TIBE STEP 



09443 
09444 
09445 
09446 
09447 
09448 
09449 
09450 
09451 
09452 
09453 
09454 
09455 
09456 
09457 
09458 
09459 
09460 
09461 
09462 
09463 
09464 
09465 
09466 
09467 
09468 
09469 
09470 
09471 
09472 
09473 
09474 
09475 
PRINT ED09476 
09477 
09478 
09479 
09480 
09481 
09482 
09483 
09484 
09485 



*S APPROACHED ONCE AGAIN AS A CCNSEQUEHCE~OF SENSING OF REVBSL09486 
H ( ^f^EP(JT)+IRDYN .EQ. C ) GO TO 3502 09487 

£° £0 3504 09 „88 

LUBAIaUE 09489 

ELEMENTS FEEL THE EFFECT CF NEU JOINT DISPLACEBENTS IN THE 09490 



319 



™«3£?J " ?c N Sr> I ii a ^J 0H CF THE MEHBES OK LI. SO STEMS HEVEESAL CHECK 09ttqi 
COflHJJMX - IS TO BE DONE CORRESPONDING 10 THIS CAS™HMcl THE nIxT STT BNT09492 

GO TO 3504 () Q ' ] T ° 3503 09493 

3503 CONTINUE °949« 

3504 CONTINUE " 1 °9«96 

KOFFCK = 

ft JaW* 1 ?.-!!*,* J GOT03350 ° * §ili§ 

sz (if = o.o XlSRl 



sqx a) =o.o 

SQY(I) = 0.0 

saz (i) =0.0 



09503 
09504 
09505 



33400 CONTINUE 1 ' "* " 09506 

33500 C^Nuf 00 

55 UoTf a'S;-}^ GC T0 33700 §f|i 

DO 33600 J = 1 10 39511 

33600 CONTInU"^ = ""■U^l 8{|]3 

33700 CONTINUE SfllS 

CALL NLSS ( LI, JJ ) HqciZ 

33800 CONTINUE ' ' Sgl'S 

COMMENT - STORE MEBEE| - END - HESTRAINTS (NONLINEAfi SPRINGS) 09520 

ST2 - Iv 1 °9521 

|$3 ; H[}] ° 9522 

ST4 = SXiMFD °,9524 



3T5 = SY(MP1i n n„c 

3505 CONTINUE ST6 = Szl& ^ 8I3|| 

IF { IRDYN .EQ. 1 ) GC TO 3515 natia 
COMMENT - SET H|HBEB END EEslBAINlS EQUAL TO 1.0E20 FCE flEHBEE SOLUTION 09529 

SYMJ = 1.0220 0q531 

SZ hi = 1.0E20 Rlifl 

sxffltn = 1.0E20 Mill 

SY BE1 = 1.0E20 R|2f| 

SZ(BF1) = 1.0E20 nl*?i. 

COMMENT - ZEEO PINNED END SOTATICNAL BESTEAINTS 09536 

IF (IPINLT .EQ. 1) SZ(1) = 0.0 09537 

IF llPINRT .EQ. 15 SZffltl) = 0.0 09§38 

COMMENT - ZERO INTERIOR STATION EQUILIBSIUH ERRORS 09539 

uu J3IU ± — J..a nusiin 



EBX(I) = 6.0 



09540 

ERY(IJ = 0.0 09542 

-351C ERZ(I) = 0.0 na^iii 

3515 CONTINUE 1 ' gflgg 

NITfljJJ) = NITB(JJ) + 1 09545 

NITMl ='NITM(JJ) - 1 09546 

KOFFSE =0 09547 

IF ( BODELI .LE. -1 ) GC TO 3519 09548 

IF I INDEX .NE. 1 [ GC TO 3519 09549 

E i^| fl ? I -'! Q jDf HE " ) G ° T ° 35151 09550*78 

iJU J3IIJ 1 — Z.REl 0Q551 

DO 3516 J = 1,«NPCS 09552 

DO 3516 K = I.MSSIin 09553 

EPR1S(I,3,K) = EPET1S(I,J,K) 09554 

-_,. „ EPR2S{I,J,K = BPBT2S(I,jJk 09555 

3516 CONTINUE * ' 0q55fi 
IF { flODELT .EQ. ) GO TO 3519 09557 
DO 3517 I = 2,MP1 09558 
DO 3517 J = 1,MNPCS 09559 
DO 3517 K = 1,flSSIHl 09560 

EPBF1(I,5,K) = EPBFT1(I,J,K) 



SLBF1(I,J,K) = SLBFT1 (I,J,K) 09562 

EPBF2 I,J,K = EPBFT2(i'j;k) 09563 

S1BF2(I,J,KJ = SLBFT2 I^j'K 09564 



09561 
09562 
09563 
09564 
09565 



3517 CONTINUE 

GO TO 35172 095fifi*7fl 

35151 CONTINUE 09567*78 

DO 35161 I = 2.BP1 09568*78 

DO 35161 J = ?;«HPCS 09569*78 

DO 35161 K = I^BSSIHI 09570*78 

351,1 CONTlful 1SlI ' J ' K > = " M1S « I ' J ' I » 3ll|I:|| 

n jsffi*? =-i%^ ' go to 3519 Ml:]* 

DO 35171 J = 1,MNPCS 09575*78 

DO 35171 | = liBSSIBI 09576*78 

E?BF1(I,J,K1 = EPBFT1 (I,J,K) 09577*78 

35171 CONTI^f lU ' J '^ -«™U:jW ojj?|j?g 

35172 C0NI ^l51B I = 2#M1 f78 8 

DC 3513 J - HS&S* 09582*78 

LIU JDIcS J - l.fflflPCS 09583 

IF ( EPSPF.S (1,1, J] .02, EPSBAX(I.L,J) ) 09584 

2 EPSHAX I,L,J) = EPSPHE(I,L,J) 09585 

IF ( SPSPRE I,L,J .LI. EPSflIN(I,i,J) ) 09586 



320 



2 EPSHIN (I,L,J) ■ EPSPRE.(I.L,J) 09587 

IF ( HO OEM .81: 2 ) GO TO 351a ' 09588 

3318 ~™™!° H(I ' L ' J) = "GBOH(I,L,J) 09589 

J3IU i-ONTINUE OQ^Qd 

3519 CONTINUE 09591 

COH.1E3T - DO FOE EACH ELEHENT 0959? 

DO 3000 I = 2, API 09593 

IM I =1-1 09594 

COMMENT - COMPUTE FOSCES ON ENDS OF DISCHETE ELEHENT 09595 

COMMENT - IT IS IXPCaTANT TO RESEMBEfi THAT ONLY DURING THE 2ND ITEHATION09596 

;=223£§! " 2£. THB WEBBER (NITM(JJ) = NITEEM(JJ) = 2 ),THE ELEMENTS FEEL 09597 

COMMENT -THE EFFECI^CF U;PDATiD % JOINT ..DISPLACEMENTS 6f THE HEMBEB ENDS 09598 

2 U1T,V1T. 

COMMENT - 5T03E " 



ITf&?5!82^«Sit"iMlif M(I,,1) '"< 1} ' DItI, ' M « 1 '' 1 - §9 9 i0 9 0%H 
.2ND FOBCES OF END ELEMENTS ONLY, FOB USE LATEB IN MEMEND09601 




IF { I .NE. 2 ) GO TO 3 52 09602 

ENDFC2 (JJ,1) = Oil 09603 

ENDFOB (JJ,2 = VII 09604 

,„„ ENDFCfi JJ,3 = 811 09605 

3520 IF { I .NE. MP1 V GO TO 3525 09606 

ENDFCH (JJ,4) = D2T 09607 

ENDFCB JJ,5 = V21 09608 

-._„ ENDFCB (JJ,6) = H2I 09609 

3525 CONTINUE 09610 

IF ( IRDYN .SQ. 1 ) GO TO 3600 09611 

IF (NITH(JJ) .NE. HNITM + 2) GO TO 3530 09612 

09613 
09614 
09615 
09616 
09617 
09618 

3530 CONTINUE"" 09620 

COMMENT - IF REVERSAL HAS NOT BEEN SENSED SO FAB ANYWEEBE, THEN GO AHFAD09621 

COMMENT - WITH EQUILIBRIUM COKPOI ATIONS. 09622 

IF ( ISVRSE . EQ. } GO TO 3540 09623 

SSS55IS " |F REViiBSAL HAS BEEN SENSED SOHEBHEBE, AT THIS STAGE. THEN 09624 

CCflJUNT - SfUP EQUILIBRIUM COMPUTATIONS. **** HOMEVEH, THE MEKBEB 09625 

SSSSgSS " Z% S 1 G 2 TROUGH THE 2ND ITERATION (NITM ( JJ) =n!tEEM I JJ) =2) 09626 

COMMENT - SO THAT SCANNING AND IDENTIFICATION IS DONE OF THOSE 09627 

COMMENT - SUBEECTANGLES OF THOSE ELEMENTS WHICH HAVE REVERSED. THIS 09628 

SR2£$S£ " ? NSUfi 2S THAT THE PBOPEB STIFfNESS MATRIX IS FOBBED IN FOEBST 09629 

COMMENT - IN THE NEXT FBAME ITERATION ( NITF = 2 ) 09630 

COMMENT - THE FOLLOWING STATEMENT SERVES THIS PURPOSE 09631 

IF f NITEBH(JJ) .EQ. 1 ) GO TO 354(1 09632 

GO TO 3b00 09633 

3540 CONTINUE 09634 

88IHK : ^!EIiT p iiIilNTl a0ILIBBI0H EBEOfiS ET S0HBIBG FCBCES 0B mil 

11 \l :lt ii-& D *o aW - EC - « EE2(1) = B1T 8382 

ERX(im) = ERX(IBI) + 01T 09639 

ERY(Ifil) = £BY(IB1J + V1T 09640 

ESZJIH1) = EBZjIMlJ * W1T 09641 



IF ( I .EQ. BP1 .AND. IEINBI .EQ. 1) EBZ(MPI) = H2T 09642 

, crA IF I .EQ. BP1) GO TO 3600 09643 

3550 EEX?I> = ERX (I) + D2T 09644 



EBY(l) = ERY(I) + V2T 09645 

,, nn „„„ EBZfl) = ERZ ij ♦ 12T 09646 

3o00 CONTINUE 09647 

IF { IRDYN .EQ. 1 ) GO TO 4300 09648 

COMMENT - SKIP FOR FINAL MESBER SOLUTION 09649 

IF (NITM(JJ) .EQ. MNITM + 2) GO TO 4300 09650 

COMMENT - THE COMMENTS REGARDING EQUILIBfilUM CALCULATIONS THAT ABE 09651 

COMMENT - PRESENT INSIDE THE DO 3600 LOOP ABOVE APPLY BERE ALSO. 09652 

IF { IEVRSE .EQ. ) GC TO 3700 09653 

IF ( NITERH(JJ) . EQ. 1 ) GO TO 3700 09654 

GO TO 4475 09655 

3700 CONTINUE 09656 

CONSENT - DO FOR EACH INTEHIOB STATION 09657 

DO 3800 I = 2,M 09658 

COMMENT - ADD STATIONS LOADS AND STATION RESISTIVE SPRING FOBCES TO 09659 

COMMENT - COMPLETE COMPUTATION OF EQUIIIBRIUH ERROBS 09660 

IF (INLOPT .EQ. 0) SQX(I) = -SX(I)*DX(I) 09661 

, EEX?I) = QXJt) - EBX(I) + SQX(I) 09662 

IF (INLOPT .EQ. 0) SQYfll = -SYfI)*DY(I) 09663 

EHYJI) = QY(S) - EBY(I) + SQY(I) 09664 

IF (INLOPT .EQ. 0) SQZ(I> = -SZ fl) *DZ (I) 09665 

SRZ(I) = QZ(I) - ESZ(I) * SQZ(I) 09666 

3800 CONTINUE 09667 

IF (INLOPT .EQ. 0) SQZM) = -SZ (1 ) *DZ ( 1 ) 09668 

'IPINLT .EQ. 1 EKZMj. = QZ ( 1) -EBZ(1) + SQZ ( 1) 09669 

INLOPT .EQ. 0) SQZ(HPI) = -SZ (MP1 ) *DZ (MP 1) 09670 



IPINST .EQ. 1j ERZ{MP1J = QZ(MPI) -EBZ(MPI) + SQZ(MP1) 09671 

COM IF (NITM1 .EQ. 0) GC TO 3815 ' 09672 

'' l APROB .EQ. PRINT ,OR. APEOE . EQ. MEMBER ) GO TC 3801 09673 

tO 3802 09674 

3801 CONTINUE 09675 

IF (IKM(JJ) .EQ. 0) GO TO 3815 09676 

COMSENT - PRINT DISPLACEMENTS AND EQUILIBRIUM EE5CRS AT FIRST INTEEIOB 09677 

COHRENI - STATIONS AND CENTEH STATION FOR HONITOE BEMBEBS 09678 

PEIHT 51, JJ, KITK1, DX(2), EY(2), DZ (2) , EEX(2), EEY (2) , 09679 

2 ERZ (21. DX(MP22),DY(MP22) . DZ (KP22 ) , ESX (MP22) ,ERY(MP22) , 09680 

J EEZ|MP22) ,DX(K) ,5y(M) ,DZ(S) ,ERX(H) ,EEY(M),EEZ(M) 09681 

38u2 CONTINUE 09682 



321 



IF (KGFFQW ,EQ. 1) PRINT 54 
IF JkOFFSe JbH: \\ PEXNT 55 
IF ( APBOE ,EQ. MEMBEB ) GO TO 38022 

COHHEHT - DUMP OF AIL STATION DISPLACEMENTS AND EOHTT TBWTny vvana <m 

S85H!f,; 1 ^U «Ilo , iIS.5B?Ji , 3IScIMSBu , H»BiS 1 f »""«"»• 

SCALE =0.0 
DO 3803 I = 1.HF1 

TE3P = DABS ( DY(I) ) 

3803 UAxUF '"' SCALE) SCLS 

2.0 



TEMP 



SCALE = SCALE 
DO 3805 I = 1,HP1 
DO 3804 II = 1,41 

ALPHA (II) = A 

ALPHA(21) = C 

IF < $£kil « G ?S 1-0D-15 ) GO TO 33804 

NTEBP = 21 
GO 10 33808 

CONTINUE 

CONTINUE** = 10 '° * DY(I) ' SCALE + 21 - 5 
ALPHA (NTEMP) = E 

3»5 2 '" «™^ ftto 'w'-'*<a' " Ill) - mm - """»• 

3815 CONTINUE 

IF { IR7BSE . NE. 
COMMENT - COMPAfiE EG.ULIBBIUB 
DO 3825 I = 1,«P1 



3804 



33804 
33808 



I G0 ' 



. 3880 
2E0ES BIIH SPECIFED TOIEEANCES 



3325 



IF (DABS (EBX 
IF (DABS (EEI 
IFfDABS (ESZ 



CONTINUE 
GO TO 4200 
3850 CONTINUE 

IF (NITM(JJ) 



.GT. 
. GT. 
• GT. 



EB1 
EE1 
E82 



GO TO 3850 
GO TO 3850 
GO TO 3850 



comment 

COMMENT 



COMMENT 
3860 



IF (NITM(JJ) .IE. MNI1M) GO TO 3880 

ilEEAlioN 'pfiOclll ° F ""*** ITEEA,II0NS S£ T IK = 

IMC(JJ) = 1 
GO TO 4250 

S0LVE H5 E - E 5 E F ° B LINEAE ifCBEMENTS OF DISPLACEMENT 



1 AND STOP 



IHC(JJ) 
GO TO 4475 
COMMENT - INCBEMENT MEMBEB DISPLACEMENTS 

DC 3900 I = 1.MP1 

j X l Z l + i (I) * 8(J) 
DYjI^ = DY(I) + B(J) 

DZJI) = DZ(I) + B ( J) 

3900 CONTINUE 
COHMENI - ZE20 EQUILIBRIUM EBBOHS AT END STATIONS 
EBXM) = 0.0 
BEX 1) = 0.0 
EHZ (15 =0.0 



EBX MP1) =0.0 
EEY (BP1 =0.0 
EBZ ?HP1j =0.0 



\L. 

NITEBM 
GO TO 3500 
CONTINUE 
IF I APBOB 
GO TO 4300 
CONTINUE 
PRINT 52, JJ, NITM1 
GO TO 4300 
4250 PEINT 53, JJ, NITM1 
COMMENT - CALCULATE MEflBEB - END 



4200 



4210 



(JJ) = NITEBM (JJ) + 1 

EQ. PRINT .OB. AEBOB .EC. MEMBEB ) GO TO 4210 



4300 CALL MEfiEND ( FMm7l6,JJ 

• NE. HNI 




- FOBCES 

2) GO TO 4350 



IF (NITM(JJ) 
U1 12) = 
V1 (2) = 
W1 (2) = 

u2(mpi; 

V2 (ME1 
il2(MPl 

GO TO 4475 
4350 CONTINUE 
CGMfiEST - SUBTRACT MEMBER - END - FOiiCES FROM JOINT EOUILTRPTTTM PKRnnq 
COMMENT - TO COMPLETE COMPUTATION OF JOINT EQUILIBRIUM EBBOBS 2BE0SS 

2 »C2S(ISII)) 2B ( fnt! < 1 >' Faa ( 4 )» JT1 ( JJ )' J *2(JJ),DC1S(ISTT), 
rnSJSIwl ~ ll°r R " SISSli ,™ £ £P ~ F0 BC£S AS BE BEES INCREMENTAL FIXED - 
8SKI I !I D N ix!°il!ilig CALCal ^ E INCBEMENTAL FIXED - END- FOBCES 



09683 

09684 

09685 

09686 

09687 

09688 

09689 

09690 

09691 

09692 

09693 

09694 

09695 

09696 

09697 

09698 

09699 

09700 

09701 

09702 

09703 

09704 

09705 

09706 

09707 

09708 

09709 

09710 

09711 

09712 

09713 

09714 

09715 

09716 

09717 

09718 

09719 

09720 

09721 

09722 

09723 

09724 

09725 

09726 

09727 

09728 

09729 

09730 

09731*71 

09732 

09733 

09734 

09735 

09736 

09737 

09733 

09739 

09740 

09741 

09742 

09743 

09744 

09745 

09746 

09747 

09748 

09749 

09750 

09751 

09752 

09753 

09754 

09755 

09756 

09757 

09758 

09759 

09760 
09761 

09762 
09763 
09764 
09765 
09766 
09767 
09768 
09769 
09770 
09771 
09772 
09773 
09774 
09775 
09776 
09777 
09778 



322 



4475 



COHfiENT 
COMMENT 
COMMENT 



DO 4400 I = 1,6 

FOMM(JJ,l/ = JEM (I) 
CONTINUE ' ' 

Ilni^SHi - GE ' 3 ■ AilD - IABAH 
STORE HEHEER DISPLACEMENTS 



.EQ. 1 ) GO TO 9900 



'' n ifj|%r3biRSSfii]W 1 ' u2> 



IF ( JNLOPT . EQ. ) GO TO 9900 

Ht M£ D ?IS BE 5- SU P p P aT SPRINGS DO NOT EIIST 
r-oMauMn. I3L ( NW BI1£ -EQ. ) GO TO 4500 

HRYM(I,J) , HHTia(I,J), 



?LJ NITH(JJ) .EQ- MNlfa+2 ) GOTO 4500 



4500 






WRITE 
2 
3 
4 
GO TO 4560 
4550 CONTINUE 
_ HRITE (N2) 

IF 

. WHITE 

4560 CONTINUE 
S3ITE (N2 



i=2,npi j 

IEIIti |I:3;S fill?! 1 IH'fi - fflU 2 fH'H - 
HJiifiS: i^lli'F B '32Jiri-fi- 



EPET2S(I,J,K) ' K = 1. 
IF (MODE LT .10.' 5 )' fco'TO 4606 
E (S2 ) (((EPBFl' (I,J,K) , EP 



' ( K 
(tf2 



{(( EPfi1S(I J K), EPBT1S(I,J,K) , 



4600 






...IF (MODEL! .HE. 2 ) GO TO $600 
BalTB (N2 ) ( ( UGEOH (I £ L t J) 



C 

COMMENT 

C 



CONTINUE 

IF ( NITM(JJ) .EQ. SNITH+2 ) GO TO 9900 



WRITE REVERSAL INDICATORS FOR STRAINS 
9900 HEII |oJTINui <<IEV(I ' L ' J, ' J=1 ' HNPCS) ' :L= ' l ' NHINGE )^ = 2»«P1) 



RETURN 
END 



09781 

09782 

09783 

09784 

09785 

09786 

09787 

09788 

09789 

09790 

09791 

09792 

09793 

09794 

09795 

09796 

09797 

09798 

09799*78 

09800 

09801 

09802 

09803 

09804 

09805 

09806 

09807*78 

09808*78 

09809*78 

09810*78 

09811*78 

09812*78 

09813*78 

09814*78 

09815 

09816*78 

09817 

09818 

09819*78 

09820 

09821 

09822 

09823 

09824 

09825*78 

09826 

09827 

09828 



******** 
SUB 

2 
COMMENT - 
COMMENT - 
IflP 
DOU 
DIH 
DIM 
COM 

2 

i 

4 

5 

6 
COM 

com 

COM 
EQD 
2 



************************** SUBROUTINE ******************** 
ROUTINE ELEMFO (DI 1 ,DY 1 , CZ 1 , DX2, DI2,DZ2, I, U1T, V1 T,H1T,U2T, 

■ ZI a EL.& an T) 

SUBROUTINE ELEMFO EVALUATES THE END-FORCES ON A DISCRETE 
ELEMNT, GIVEN TEE ELEHE ST-END-DISPL ACEHENTS 
LICIT EEAL*8 (A-H,0-Z) 
3LE P2ECISI0N DCCS,DSI 
ENSION D(6,6 

CUEVAT(22). GABBA(22), BBS(22), 

22), SX 

QY( 225, QZ 

ERX I 22 
SQZ( 22 
V2 ' 



DCCS,DSIN,DATAN 

NSION CUfiVAT(22). GABBA(22). 
HOB /BLOCK7/ F( 22) , AE 

DZ 

Bflis( 22), 
XL,XR,X1,X2, 



/BLOCK7/ F 22), AE( 22), '5X( 22), ST ( 22), 

22), Oil 22), QYJ 22[: 02? 22V I DXJ 22[. 

I 22[. DZ] 22[. Eiif 22f, ERY( 22f, Efii ( 22/, 

XI 22}, SQY( 22), SQZ \ 22 , 01(22), V1 ( V 22) , 

le? 2 U, UL 2 , 2 U. ih.m'. W2 22 DS 3,3 '22) 



SZ( 22 
DI( 22 
SQZ{ 2 
Vi 22) , 
Bats] 22) 
HON /ELK 2/ 



i( 22 22f 



SHS(22) 
' 22) 

22) 
( 2' 

22) 

22) 

22 



,TH,HSQ,HCD,X2L,I1,I2,NQ 
C0EVA1 (22) , CDHVA2(22] 



IVALENCE (CUEVAT(I) .CURVA1 (1)) , ( GAMM A ( 1) , CURV A2 (1) ) 
(BHS(1) ,BHlS(1)) , jSBS(i) .SM2S Of' 
DATA PDNO /4HPDNC/ e PDN /4H PDN/ 






COMMENT 



200 
COMMENT 



MON /SKT23/ PDEL$A 
HON /SKT29/ E?SL0N(22) 

'CUEVAT (1) . CU«. 
BKS(I) ,BH1S(1) ) 
u*+~ PDNO /4HPDNC/, 
DATA SHEAS /5HSHEAB/ 
IF (ELEMNT .EQ. SHEAR) GO TO 3000 
COMPUTE TBE ELEMENT DEFORMATIONS 
DDI = DX2 - DX1 
DDK = DY2 - DY1 
IF ( PDELTA.EQ.PDNO -OE- PDELTA.EQ- PDN ) GO TO 200 
GO TO 300 
CONTINUE 
COMPOTE DEFORMATIONS BASED ON SMALL DISPLACEMENTS 



30G 



S 

DELTA 
THETA 

GO TO 400 

CONTINUE 

COSIM1 

COSI 

SINIK1 

5INI 

COSCCS 

SINSIN 

E = CDX 



DDY 
DDX 
S / 



- 0. 5 * H * ( DZ1+DZ2 ) 




DZ1) 

DZ2) 

DZ1) 

DZ2) 
+ CCSIM1 
+ SINIB1 



+ K* (1.0 - 0.5*COSCOS) 



************* 
V2T, 09829 

09830*11 

09831 

09832 

09833 

09834 

09835 

09836*13 

09837 

09838 

09839 

09840 

09841 

09842**5 

09843 

09844 

09845 

09846*13 

09847*13 

09848 

09849*16 

09850*10 

09851 

09852 

09853 

09854 

09855 

09856 

09857 

09858 

09859 

09860 

09861 

09862 

09863 

09864 

09865 

09866 

09867 

09868 

09869 



323 



o 



THETA = DAlXN(lTBfelA) nlVll 

SI NT = 3/(8 + DELIA)' IVenl 

400 C0.TlS8| T ■»*«/«■ ♦'»"»> 0||?| 

5iSi : T Df?-"THElA ollll 

COBHENX - STOSE e |T|AIH AND THE lie CUEVATURES OF EACH ELEHENT FOE OUTPUT09879 

ggSSMlS! - tadi /s SfffS 



COEVAi I = TAU2 / H 09881 

comem^call MflSMonionjniiwoKis II lUiiR.n.siMn 81111 



L FAEEEV (DELTA, TAU1. TA02 I D TT Shi n 
GO TO P 600 TA ' BQ - PDSO '°8- PDELTA,EQ.fDN', T l6 TO^Oo' 

rnu TT«nr 



TO <: 600' L ' , * iiy ' r " BU " UB " * BBJ,M » B fl«W» ) SO TO 500 09885 

500 CONTINUE 0gg§6 

SI? : y« - mi ) / h 81 1§2 

V2T = -»1T 09889 

Oil = -02T 09890 

SIT = -BM1 + 0.5 * V1T * H nllll 

GO Xo'lSoO BK2 + °- 5 * V1T * H BI11I 

600 CONTINUE 09894 

XI™ = il B2 ~ flB1 ) /1H + DELTA) nqaqfi 

U2T = TT*C0ST + VT*SINT SIfI| 

m z im iwi - vt * cost siiii 

V1T = -V2T 09899 

S1T = -BH1 + 0.5* (- U1T*SINIS1 + V1T*CCST?m *H noon? 

CO MaE ,T - STOEE^B^asl^E^LT U1I * SINI + ? "* C ^ 1 ^ 

?000 NT " CCNTINn| ALI ' Y BH1 & 3H2 ABE ALS0 510? >™ FOfi 0DTPaT DEPOSES. 09904*90 

£8 1188 I : H Silo ! 

plijij = BHl 09909 

GO TO B ilf| lJ = EH2 0°9 9 9 9 1 1 ? 

3C00 COKTINUE RII31J38 

COKJ1ENT - COMPUTE ELEH2NT DEFCRHAIIONS nQQi?i* 1 ,n 

DDX ■ DX2 - DI1 OQOllIiS 

DDT = DY2 - DX1 nqqll*1n 

DDZ = DZ? - 1171 09916*10 

uuu UA^ U41 09917*10 

GC tTOSo ' EQ * PDB ° • 0B * PDE L TA .«0. PDN ) GO TO 3200 09918*19 

3200 CONTINUE RSlU 9 *'' 9 

COMMENT - CO "DTE e D|FOBHMICHS BASED ON SMALL DISPLACEMENTS 09921*1? 

DELA = DDX SI 9 ^ 2 ,!] , 

Mil = DZ1 - THEIA nqq 2 U*^ 

PSI2 = D22 - THEIA filoitllS 

SIle I ^z PSI1 + PSI2) 81111*10 

GO TO 3400 09927*10 

3300 co.™ m th ddx gilllili 

COST = DCOSiTHETA ollfsJlQ 

COS1 = DCOS PSI1) rtQoill^I 

COS2 = DCOS PSI2 0II17JH 

SIH1 = DSISi'PSH nqqi«*ia 

SIN2 = DSIN PSI2 nqq^q*iq 

COSCCS = CCS1 + COS2 nttantU 

SINSIN = SIN1 + SIN2 nqquiJiq 

DELA = THDX/CCST - H*CCSCOS ollttJIll 

DELS = H*SINSIN nqq^*i6 

3400 CONTINUE 2 9 , 9 ," 4 :* 19 
COBBENT I loi 2 OOT?D Ai S SHEAB STBAIKS *»>> * HE CUBVATURE OF EACH ELEMENT 09946* 2 

gi*S«ij : Slifcil gflsiJjo 

MM ^^,siitcMHfihtt.35H.3s:iip IN S3EAB 2lesent Hi !S:ii 

GO ^0 3600 * EQ * PDN£ -° B - P " £tA :EQ - Pfi » I GC T0 3500 09953*19 

3500 CONTINUE SllllflS 

U1T = -TT 09955*19 

ViT = SH 09956*10 

HIT = -BH + H*SH Silted 

rj2T = tt 09958*10 

V2T = -SH 09959*10 

H2T = BE ♦ H*SH Sflt?t^8 

30 TO 4000 J? 99 ? 1 * 10 

3600 CONTINUE 8IIHJ1Q 

DELAE2 = DELA/2.0 nqq^*io 

OELSD2 = DELS/2.0 09965*21 



324 



4100 



9999 



DELAD2) 



COMMENT 

COMMENT 

4000 



D1T = -TT*CCST - SK*SINT 

VI T = -TT*SIKT + S3*C0ST 

«1T = -BH + SH*(H*CCS1 + DELAD2) 

TT*(H*SIN1 - DELSD2) **•*"*> 

02T = -U1T 

V2T ■ -V1T 

H2T = BM + SH*(H*COS2 ♦ 

,.,„„ T T *(B*3IN2 - DEIS132) 
STOEE FOB USE BY ELEHST 

CONTINUE* 11 " 2 TT ' BS S SH ARE SI °2SD FOB OUTPUT PURPOSES 
DO 4 100* J = 1,3 
DO 4100 K = 1*3 

DS(J,K,I) = D(J,K) 
TTS 11) m TT 
I) ■ BH 
I) = SH 



3MS 

SHS 

CONTINUE 

EETUBN 

END 



09966*20 

09967*20 

09968*20 

09969*20 

09970*20 

09971*20 

09972*20 

09973*20 

09974*19 

09975*19 

09976*19 

09977*10 

09978*10 

09979*10 

09980*10 

09981*10 

09982*10 

09983*10 

09984 

09985 



******************** 

SU3EOUTINE HEME 
COMMENT - MEMEND EVAL 
IMPLICIT HEA1*8 
DIMENSION FMB(6 
COMMON /BLOCK2/ 

2 DC2S { 25) , 

3 PRAGJ25), 

4 IO?OP( 25), 



SAL~( 25) 
5 NSXB( 25 



COMMON /BLOCK7/ 

2 SZf 22) , 

3 DYJ 22J . 

4 S2X( 22) , 

6 BM1S ( 22) , 
COMMON /BLK1/ 

2 KE2P2, 

3 K2EP5B, 

4 NCD3B, 

5 NCD5D, 
o IABAN, 

7 MP1, 

COMMON /BLK4/ S 
COMMON /BLK6/ Q 
COMMON /BLK7/ I 
COMMON /SKT9/ 

IAXCPT 
COMMENT - MAKE 



****** 

ND ( ? 

UATES 
(A-H, 

),SA<3 
DXS ( 
PRF( 
ELEHN 
IPINL 
NSXL 
NSYE 

e i 2 - 
QX( 2 
DZ( 2 



. NSXL( 25) , 

5 . NSYE? 25) , 
tV F( 22). 

li. 



******** SUBBOOTINE 

MM,L6,JJ } 

THE TOTAL FORCES ON 

slj^'DYsfi? 

m. P£Al(2 

L?5) , IPIHE(_25) 



25) 



m { 2 

BM2S( 

TOL, 

KEEP3A 

KEEP5C 

NCD4A, 

NCD6, 

IFORM, 

MP2, 



11 

2 22) 



NSYL( 
NSZfij . 
AEf 22) , 
QY{ 221. 
E2X( 22), 
SQZ( 22 
V2{ 22) 



I 

CS I 



2=1 : 



U 



TH 

ZLS 
QM( 

NC5 

NSZ 

NCD 

SX< 

QZi 

EHY 

U1 

B2 



******* 
E ENDS 



************** 
OF THE HEHBEHS 






22), TTS( 22), AG 

ELEMNT,NJST, KEEP3C, 

,KEEP3E,KEEP4A,KEEP4B, 



D3C, 



,KEEP5D, KSEP6, 
NCD4B, NCD4C, 
SCD7, IP8, 
BH, NJT, 

ISTT, LTT, 



KEEP7, 
NCD5A, 
IP9, 

NST, 
ITYPEL, 



T1,ST2,ST3,ST4,ST5,ST6 
i 'z9 i 2,QT3,QT4'qT5'qT6 
NLOPT, If AE, KCFFJ,K0FFQV, KOFFSE 



22 

22 

22 
NCD3C- 
KEEP4C, 
NCD2, 
NCD5B, 
IP 10, 
NLT, 
ID J, 



DC1S{ 25) , 
WM( Z5), 

INLOP f 25) , 
NAfi{ 25) . 
IAXCPS( 25) 
SY{ 22) , 
DXj 225 , 
EBZ( 22), 



71 ( 22) , 
DS(3,3, 



KEEP5A, 
NCD3A, 
NCD5C, 
ITYPE, 

B * 
NSTL 



22) 



********** 
09986 
09987 
09988 
09989 
09990*42 
09991*42 
09992*42 
09993*42 
09994*42 
09995*42 
09996 
09997 
09998 
09999 
10000 
10001**5 
10002*79 
10003*61 
10004*61 
10005*61 
10006*61 
10007*61 
10008*61 



COMMENT 
COMMENT 



USE OF 

U1T 

V1T 

If II 

U2T 

V2T 

K2T 
ADD ON THE 
FOECES ON T 
IF (INLOPT 

IF 



ENDFOfi j50.6) 
= IAXOPS(ISTT) 
THE RELEVANT END FOECES THAT HERB 



fmm (1) 

(INLOPT 
FMM (2) 
IF (INLOPT 
FKH (3) 
IF (INLOPT 
FMM (4) 
IF (INLOPT 
FSH (5) 
IF (INLOPT 
FHM (6) 
EE1UBN 
END 



ENDFCE (JJ,1 
ENDFCR JJ,2 
ENDFOE JJ.3 
ENDFCfi iJJ,4 
ENDFOE iJJ,5 
ENDFOE (JJ.6 

LOADS ON THE END-STATIONS AND 
HE END-STATICNS 
.EQ. 0) SQXM) = -ST1*DX(1) 
= U1T - SCX(1] 



.EQ. 0) 

= V1T 
•EQ. 0) SQZ(1 

= KIT - SQZ('1) 
.EQ. 0) SQX(MP1 

= U2T -SQX{MP1 
.EQ. 0) SQY(HP1 

= V2T -SQI(BP1 
.EQ. 0) SQZ(MP1 



QT1 



J' 

ci(i) - . 

54U. " ~ST3*DZ(1) 



;QY(1) = -ST2*DY(1) 
SQYH) - QT2 



B2T - SQZ(MP1) - QT6 



QT3 
= -ST4*DX(MP1) 

- QT4 
= -ST5*DI(MP1) 

- QT5 
ST6*DZ(MP1) 



10009 
10010 
10011 
10012 
10013 
STORED IN HEMSOL10014 
10015 
10016 
10017 
10018 
10019 
10020 
THE BESISTIYE SPRING 10021 

10022 
10023 
10024 
10025 
10026 
10027 
10028 
10029 
10030 
10031 
10032 
10033 
10034 
10035 
10036 



****************** 

SUBEODTINE AD 

COMMENT - SUBEOUTIN 

COMMENT - COOBDINAT 

COMMENT - EBBOE FOB 

IMPLICIT SEAL 

EEAL*8 JTSHE, 

DIMENSION FT 

DIMENSION DC 

DIMENSION TBD 

CCBECN /BLOCK 



QZZ(2b) , 
DYY{25[, 
ERXX (25) , 

"111!; 



**************** SUBROUTINE *********************** 
JTEB (F1M. F2M, J1, J2 , DC?. DC2) 

| AD JTEB TBANSFCfiMS MEMBEB-END-FOECES TO ST2UCTUEE 
ES AND SUBTRACTS FBOB APPROPRIATE JOINT EQUILIBRIUM 

r cAHE 
*8 (A-H.O-Z) 
JSYES 
K(3), F2M(3), F1S(3), F2S(3) 

(4,i) ^IBDT (4, 4) / F1S4 (4) 



1/ 



NSXX 
NSYP 



SXX (2 5 
DZZ (25 
EEYY(2_ 
tiSYY]2 5i , 
ISTJE (25) 



1^25) 



<) , Si\ (25) , 

\. EXX]25[, 

!5), ERZ2(25), 

NSZZ 25), 



F2S4 (4) 
QXX(25 
SZZ 

RYY 
QMJ 
IMJ 



25] ; 

25), 
25 , 
25 , 




********** 
10037 
10038 
10039 
10040 
10041 
10042*75 
10043 
10044 
10045*75 
10046 
10047 
10048 
1C049 
10050 
10051 



325 



SVV(25), DVV(25), EBVV(25), 



2 COHHON /BALA0 1/ QWf25L. 

2 n *ffi&w%Timii \am im -,um a fjvt ( 25) - 



'oi.iLi/ iui., BiiJSBB'i. NJST, KEEP3C, NCD3C 

KEEP2, KEEP3A, KEEP3B, KEEP4A .KEEP4B. KEEPUC KFwp^a 

KEEP5|,KEEP5c;kEEP5e;keEP6,'kEeI7:'nCD2. NCD3A ' 

NCD5n' SSfil** SSS3 B ' ?S8 4C » NCD5A ' ^DSB, NCD5C,' 

NCDbD, NCD6, NCD7, IP8. IP9. TPIfl ttvdf 

IABAN, IFOHfl, NB ' lW, \lh HLT,' B* ' 

MP2, .ISTT, LTT, _ITYPEI,IDJ. NSTL 



DATA JSYES /5HJSYES/ 
COBSENT - FOHH TRANSPOSE OF HEHBEH TRANSFORBATION KATBIX 
IX, 1 ( i # 3) = 0.0 



COBKENT 



DCT (2,3 
DCT (3,1 
DCT (3, 2 
DCT 

DCT 
DCT 
DCT . 
DCT (2, 2 

TRANSFORM HE 



= 0,0 

= 0.0 

-,-, = 0.0 

3.3) = 1.0 



1.1 
1^2 



= DC1 
= -DC2 
= DC2 
= DC1 

CALL flATall B iDcf!!?U?i?if 5T FE ° M J ° INT T ° STRUCTURE COOBD 

COMKEa CA£L IaANSP0 15TH31 B (rc| N ?iH F2S) " T ° J ° INT T ° STHDCTtJ ^ COORD 

IF (JTSBfi .EQ. JSYES) GO TO 100 
COBBENT - ACCflflOLATE JOIBT EOHlLIBHIOa EfifiOB AT BEBBEBS FfiOB JOINT 

ESXXIJ1) = EBXX(JI) - FISH) 

ERYYJJ1) = ERYY(JI) - F1S(2) 

EHZZ(Jl) = EBZZ(J1) - F1S?3> 

COBBENT - ACCDHDLATJ JOINT SQUILIERIUB EI 



ERXX(J2) = EHXX(J2) - F2S 
E3IYjj2) = EBYY J2) - F2S 



?BOR AT BEBBEBS TO JOIST 
i 



ERZZJJ2J = Efizz)j2[ - F2Si 
IF ( ITYPE -LE. 2 ) <3C TO 140 ' 
COBBENT - STORE CONTRIBUTION OF BEBB2B END FCBCPq 4TDKP th s cdc-tit 
COBBENT - JOINT EEBCS VECTOR FOB USE IS DYNAKIC PRC3IEB cSly SPECIAL 
COHBENT - (USEFUL IN CASES WHERE JOINT HAS A LARGE APPLIED FOBCP 
COHBENT - TO CONTROL A DISPLACEMENT OB AH ACCELERATION ) 

ERXXDN(J11 = EBXXDN( 

ERYYDNJJIJ = ERYYDN(J1) - F1S(2i 

ERZZDNJJlJ = EBZZDN(J15 - F1S 3 



100 



CALL 
CALL 
CALL 



ERXXDN 
ERYY 
SBZZ 
GO TO 140 
CONTINUE 
IF (JST(JI) 
(DAiiS (EC 
(DABS j"" 



SDN(J1) - F1S(1 

CDNJJ1J - F1S{2 

ZDN(J15 - F1S(3 

DN (J2) = EBXIDN(J2) - F2SM1 

DH|j2| = ERYYBN J2< - F2S 2 

Bb|J2) = ERZZDN(J2) - F2S(3) 



IF 
IF 



•EQ. 0) GO TO 1 10 



EC1 .QT. 0.99) KEY=1 
J.DC1J .LB. 0.99[ KEY=3 
TB!nsFH (K£Y,J1,TBD,3,4) 
TRANS? [TBD'|B£T.3;«/ ' 
BOLT (TRDT,F1S,Ffe4,4, 



i-ai-i. BULT (TRD1.F1S.F1S4 4 3 11 

COBBENT - ACCUBOLATE JOINT ta£lBRIu2i|ll S AT BEBBERS FROB JOINT 

ERYY J1) = ERYYJJ1) - F1S4(2 
EBZZ(J1J = E£ZZ(J1J - F1S4J3) 



IF ( 



|5,^] J1 i- = E EVV i3 l5 - F1S4(4l 

ITYPE 



10 10 120 
ERXXDN(J1) - 
ERYYEN(J1] - 
ERZZEN(J1) - 
EBVTDN(J1) - 



110 



120 



IF ( 



X (J1) = ERXX(J1) - 

Y(J1J = ERYY J1) - 

ZJJ1) = ERZZJJ1 - 

PE .IE. 2 T GO 10 1 



F1S 
F1S 
F1S 
20 



ERXX(J1 
ERYY 

ERZZ 

2 I - 

= EBXXDN{J1 

= £RYYDN(J1 

= EBZZDNjJI 

0) GO TO 130 



F1S4 
F1S4 
F1S4 
F1S4 



F1S 
F1S 
F1S 



ii 



.IE. 
EBXXEN (J1> 
ER YYDN(J1) 
EEZZDN(J1) 
ERVVCN(J1J 
GO TO 120 
CONTINUE 

ERXX (J1J 
E3Y1 
EHZ1 
ITYPI 
ERXXEN (J11 
ESYYEN (Jlj 
EBZZDN (J 1] 
CONTINUE 
IF (JST(J2) .EQ. 
IF (DABS(EC1) "( 
If IT" ' 
CALL 

CALL TRANSP tTSSItSif «3Uf 

CALL BULT (TRDI.F2S F2S4 4 3 li 

COBHENT - ACC "^ATE JOINT ECOlflBRrfH^lBfcB AT BEBBERS FROM JOINT 

ERYY J2) = ERYy!'J2'i - F2S4 (2 
EEZZ (J2J = EEZZ(J2'i - F2S4 (3 

EBVV]j2'i - F2S4(4) 

2 1 GO TO 140 

= EBXXDN(J2) - 

= ERYYDN(J2) - 

= ERZZEN(J2) - 

= EBVVDN(J2) - 



DABS(e£1) .GT. 0.99) KEY=2 
DABS(DC1) .LE. 0.99< KEY=4 



IF ( 



GO TO 



EEVV (J2) 
ITYPi ,Le. 
EBXXDN (J2) 
ER YYDN (J2) 
EEZZEN (J2) 
ESVVDN (J2) 
140 ' 



F2S4 
F2S4 
F2S4 
F2S4 



mum 

10054*79 

10055*80 

10056*82 

10057*82 

10058*79 

10059*61 

10060*61 

10061*61 

10062*61 

10063*61 

10064*61 

10065*82 

10066*75 

10067*75 

10068 

10069 

10070 

10071 

10072 

10073 

10074 

10075 

10076 

10077 

10078*75 

10079*75 

10080*75 

10081*75 

10082*75 

10083*75 

10084*75 

10085*75 

10086*75 

10087*75 

10088*75 

10089*75 

10090*75 

10091*75 

10092 

10093 

10094 

10095 

10096 

10097 

10098 

10099 

10100 

10101 

10102 

10103*75 

10104*75 

10105*75 

10106*75 

10107*75 

10108*75 

10109*75 

10110*75 

1011 1*75 

10112*75 

10113*75 

10114*75 

10115*75 

10116*82 

10117*82 

10118*82 

10119*82 

10120*82 

10121*75 

10122*75 

10123*75 

10124*75 

10125*75 

10126*82 

10127*82 

10128*82 

10129*82 

10130*75 

10131*75 

10132*75 

10133*75 

10134+75 

10135*75 

10136*75 

10137*75 

10138*75 

10139*75 

10140*75 

10141*75 

10 142*82 

10143*82 

10144*82 

10145*82 

10146*82 

10147*75 



326 



130 



CONTINUE 
ERXX 



IF ( 



140 



EETCJBN 
END 



(J2) = EHXX(J2) - F2SM) 
J2j = ERYY J2 - F2S 2 
(J2) = EEZZ(J2? - F2S{3) 
S .12. 2 ) do to 140 



,J2) = EHXX(J2 
EEYY(J2J = ERYY(J2 
EHZZ (J2j = EEZZ(J2 

" 'E. 2 ) SO tO 140" 

= EBXXDK(J2) - F2S 
= EBYYDN J2) - F2S 
= 2BZZDN(J2) - F2S 



ITYPE 
EBXXDN(J2 
EEYYDN (J2 
E3ZZDN (J2 
CCNTINU 



10148*75 

10149*75 

10150*75 

10151*82 

10152*82 

10153*82 

10154*82 

10 155*82 

10156*75 

10157 

10158 



********************************** SDBRonTTNP ***** 
SOBflODl'IHE PBINT9 (AN2 HPEOR MSfl 8 SHl fj 

EEAL*8 JTSHfi,JSYES 
EEAL*4 DISJT 

BEAL*4 POSCBL, STBAHL, BflOHNL, CUBVAL. 
3 POECEB, 5TBANR, BflOBNa; COSVAR; 

3 ££maxf, fhmaxd, fbbbcm; FRBBOT, 

5 shhjt' toaxd ' TOBOfl ' iohoi,' 



****************** 
L4,16) 



SHF02I, 
SHFOBB, 
FBHSHF, 
TOSHF, 



GABMAL, 
GAHBAR, 

FRBLTD, 

TOITD, 



DIMENSION 38X16,1.4), HO (L6) , »(I6) 

22^ GASBA(22) , BBS 



DIMENSION ANi(l1 
DIMENSION ALPHA (4'1)~ 



COBBON^BLOCKI/ X(2$£ ,"" 



QZZ (25) , 

DYY(25i, 

ERXX (25) , 

NSXX (25) , 

NSYPJ25) , 

COMMON /BALA01/ 



COHilON . 
2 DC2S 

4 IOP 

5 NAL 
6 

COMBOS / 



DZZ 
EEI1.. 
NSYY{25i . 
ISTJE (25) 
QVV(25) . 
nsvv(25j 



EVV(25), NSVV(2Sf 

/BL0CK2/ DXS( 25), 

-JSf 25) , PHF 25[; 

PEAGJ25) 1" »•&«?*£#' 



EL£l5N{25[, 
IPINL 25) , 
NSXL( 251 
NSYRj 25 



NC51 
NSZI 
NCDS 



01? * .25), 

«j.| 251, NSXLf 25) , 

NSXK( 2>\ t NSYBj 25), aM1 

jCOB-OJ^feotiv ™|y §0.6, ^"^50,21^,^50,^ 



SYY(25J , 

EBZZ(25), 
NSZZ(25), 

SVV(25) , 

DYSf 25), 
PBAE( 25) , 

IPINB( 25) , 
NSYLf 25) - 
SSZB( 25) 




QYY (25) , 
DXX(25J ' 
RZZ(25) , 
WHJ 25[, 
NSXP(25) , 

ERVV (25) , 

DC15( 25) , 
SH( 25) , 

INLOP ( 25) , 
NAB( 25) 



COaHON /BLOCK7/ 
SZf 22) , ' 
DY( 22), 
SQi(_22[ # 



( 22 
SQY( 2 
Q2{ - 



u 

DZ 



if. 



BB.2SJ 2$ 

ACCJT (10. 

,FACCJT(10 




r VELJT(100 
,FDAaJT(" 



luif -FDAflJl ( 100) ,CDA 
TOL, E1EBNT, NJS1, KEE^3C, 



*'T( 22) , 
6 BMlSf 22) . 

common /3L0C21/ 

2 DVELJT(100) 
CCM.-10N /3LK1/ iul, JSi.JSBHT, KJ51, KEEP3C. 

i Hllit kS e p1 a 'Keep3e;keep4a,keep4b, 

3 KEEP5B,KEEP5C,KEEP5E,KEEP6, KEEP7, 

4 NCD3B, NCD4A, SCD4B, NCDUC^ NCD5A^ 

5 NCD5D, NCD6, NCD7, IP8, IP9, 

6 5*3AN, IFOBB, HH. NJT, SST. 

1 BP1, HP^, ISIT, LTI, ISYPEL. 
COM HON /BLKV XL,XS,X1,X2, ' H.TH.HSQ 

•, COMH 2L<§ L 5 3 ^c- HNJT / HNS$ ^ Sl ' T ' H N"-HNC§,MRC6, 

2 HllPCS,BNSS,BNQBB,BlJJST,flNJSS 
LOHBON /BLK5/ NFSDB .N ITF, N1 , N2 

COHflOfi /BLK7/ INLOPI.IFAE # KCFFJ.KOFFQ»,KOFF 
COHKON/ITC/ Eafi1.2fifii,EBljBB2 f D$I,cS,Sfl,aB 
2 aNITM.NSMJ.NSBfl ' 

COKKON /MABN/ NJNC,NBNC 



25), IAX0PS( 25) 
5),VIJ(25),VDJ(25), 

LT(50) , 
IBC(50) 

SY ( 22) , 
dx] 22[; 
EBZ( 22), 
»1 (22), 
DS(3,3, 22), 

bTIOO) .DACCJT(IOO) . 
«^]00f^ISJT|80,7i) 

KEEP4C,KEEP5A, 
NCD2, NCD3A, 
NCD5B, NCD5C, 
IP10, ITYPE, 
NLT, B, 
IDJ, NSTL 

,HCO,X2L, 11.12, NO 
HDJT,HNJS,MNE,BNCS, 

SE 

(20) ,BJ(20) ,BNITF, 



cc 



SBON /SKT2/ 
HRT (25,10), 

WRTYP'T" 



KETY (25.10) . 
WRTYP(25, 10/ 
COBKON /SKT5/ 



SHX(25,10 

«BXP(25,1. 

ifiTZ(25,10 



HEY(25.10), OEZ(25,10), 
HEYP(25,10S, SBTJ?(2$.l6f , 
,10), HETXP(25,10) , 



HBIV(25 



COKBON 
COMMON 



/SKT1 1/ 
/SKT13/ 



KBXB 

«RT 

HSS 



5«{il'1S}» BBIH ( 21 »10)» "EZB (21,10), 
XMpl.loJ, 8||YMJ2i;iSj; IBTZB-klllor 



COHMON /SKT15/ 
COaSON /SKT22/ 
COBfiON /SKT25/ 
COHMON /SKT26/ 
COHMON /SKT27/ 
COMMON /SKT28/ 



EPS1S(21,10,3) ,EPBI1S(21 
EP22S(21,10;3) ,EPRT2S(21 



,10,3) 
,10,3) 



CUHVAL(2G,71 
i CtJEVAa(20,71 

FEBROT(20,71 
T0AXD(2U,71)', 
TOLTD(20,71 
COaaOH /SKT29/ t£ 
COMMON /SKT30/ 
COBMON /SKT32/ 



JJ 

TIME, JT, IfiDYN, IHSTEE(71) 

ITSLEF, ITS5GT, SIE, NRE ' 

LTYPEL 

IEEAD, IHSITE 

?P E ??I- 120,71) t STBANL_(20,_71) x BBOHHL (20 ,71 ) 



r FCHCEB 

, FKBAXF 

.FEHSHF 

TOBOB( 



/ 1 1 , z 

[20,71 

20,71 

20,71> 

S3, 71)', 



STRANE 
..FEB AID 
,FEHLTD 

TOBOT ( 




^PSLCN (22) 

MS0;iF(25) 
EPBF1 " 
SLBFT1 
SLBF2 



C027A1 (22) 

BL0AD(25) 



oauaui. i zu , / I ) . 
1) ,BBO«NS(20,71) , 
1) ,FRHBOM]20.71) , 
1 ,TOAXF (20,71) , 
), TOSHF (20,71) , 

A2(22) 

25 3) 



(21,10,3), EPBFT1 (21,10,3) , SIBF1 (21 10 3) 



********** 
10159*74 
10160 
10161 
10162*75 
10163 
10164*82 
10165*82 
10166*88 
10167*88 
10168*88 
10169*74 
10170*56 
10171 
10172*13 
10173 
10 174 
10175 
10176 
10177 
10178 
10179*70 
10180*75 
10181*42 
10182*42 
10183*42 
10184*42 
10185*42 
10186*42 
10187*82 
10188*82 
10189 
10190 

10191 

10192 

10193 

10194 

10195 

10196**5 

10197*85 

10198*88 

10199*79 

10200*61 

10201*61 

10202*61 

10203*61 

10204*61 

10205*61 

10206 

10207 

10208*79 

10209 

10210 

10211*88 

10212*88 

10213 

10214*84 

10215*84 

10216*84 
10217*84 

10218 

10219 

10220 

10221 

10222 

10223 

10224 

10225 

10226 

10227 

10228*88 

10229*88 

10230*88 

10231*88 

10232*88 

10233*68 

10234 

10235 

10236 

10237 

10238 






327 



11 FOBMAT 

15 FOEMAT ( 

51 FOAM AT 

52 FOBHAT 

53 FOHflAT ( 

2 * 

54 FOBMAT ( 
2 v 

61 format 

2 
71 FOBHAT 

2 
81 FOBHAT 
91 FOBMAT 

2 



I lllo^ilhi'M: KiSSBI'HM' Epspa M2i, 2 .io), 

COflHON /CHAN1/ JTSHB lz, '^' ,u '' ««»IW*U1,i # 10J 
COMMON /CHA13/ GAHES(25,3) ,GAHBTS(25.3) 
COMMON /CHA28/ SflFOEC (26, IV 2?i - - l - •* -' 
2 GAHHASj[20,7 1 

(CUBVAT (1) ,CUBVA1'(1) ) , ( „.,■•-■ 

III ffihfF&i&h&L- 

40H TABLE 9 - HEMBEB RESULTS (CONTD) / 1 

111 PHOBLEH L *n T ° F HEMBEfiS Q"" C " fiVE EXCEEDED ON THIS, 

321 EXCEE; E D LI a i T TH Is B I^l!I H) ST8ES5 - STfiAIfi CBEVE ' 
1§B HEHBEB N0HBEE,I5,15H STIFF TYPE. 15 

15H LOAD TYPE , IS ) *>±*rjr iI "' n ' 

jji v s n a .\&h*f 13H alphi ■ - E11 - 3 ' 
111 ir ^iin^sL^^is lU'M S8is;"is; 5) 

25H ALONG THE HEMBEB AXIS j rnvjn " u -»- a -ir "# 

HEHBEB. DID HOT CONVERGE AT END OF SPECIF, 



;AHRS(25.3) .GAHBTS(25,3) 

./, : ?!igi??iJHi } GAMAlt4o ' 71 J' s " o «<2 o »^)» 

TABLE 9 - HEMBEB RESULTS (CONTD) 



99 FQgjU| (//,50H *** HEHBEB PIP 



10 V° EHAT 30 H hSIIbCI TO^IhPIIIIeI^II AN ^"PLACEHENTS ABE «ITH, 
30H JHJ X ""S|j||i&- 21X ln2™Hfftff ROTATIONAL 



A 5X, 

A 52, 



3 

4 

5 

b 

7 
210 FOB 
220 F05MAT 

2 4HT_ 
230 FOBHAT 

2 
240 FOBHAT ( 

2 //.5X, 

250 F0E3AT f 
777 FOHHAT { 



468 
158 



S BEfi L AXEi P ^,' F B C "l-! E 3ITH EE3PECT T ° THE ' 
10H AT JOINT , 15, 12X* IOh'aT JOINT 15 // 51 

58 slUk F ° BdE S 'Itt'hW Jsfilhl FOB^'i X ; B 11„ 
Ijo bHEAn = ,E11.3.5X. 15H SHFAB - t? 1 i a 
158 HOHENT = '.SUli'M', 158 HOHENT = 'JH'A', 



3. 



4T (///,5X, 13HHEHBEB NUflBEB, 15) 

i / ^'i^ 1 ^? BEBBEB "UHBEB,I5,10X,12HTIHE STEP ,15,51 



T*-\ / t<,'£ii 'Jfl3-6nBCK NUBBEE,I5, 10X,12 
xn-E,oX ,F 11. 6) 

T (///,5X, 13HHEH3EB LENGTH, 710, 3 ,5X, 
11HELBNT LNGTH,F10.4.//) ' * 



..14HN0HBEB CF ELEH,I3,5X, 

fi^A^I* 5 Fi^??'lli^ 1HFI3ST HINGE, 13X, 12HSECOND HINGE, 
548N0JB AXIAL FCEC AXIAL STRAIN BENP HOHENT CUBVATDBE 



28B BEND 
5X, 12, 3X, 2 
48H *** 



HOHENT CUBVATDBE,///) 

( 2 (1PE11.3),3X), 2 (1PE11 

^LOTION DID NOT 



2 10H DATA *** 

300 FOBHAT ( 6 (,/) ,51, 4 8ELEH, 
2 // , 5 X , 



SCI 

J 



CLOSE 



STUDY' HONITOB, 



) 



CCHHENT 



780 
7cJ5 

coaaENT 

COBHENT 



790 
COMMENT 
COBHENT 



IF 

STO 

IF 



800 



2 
3 
900 

910 



54|ifiaE AXIAL FOBC AXIAL STRAIN BEND HOHENT CUBVATUB 
4X,25HSHEAB FOBCE SHEAB STBAIN,///) 

DATA A.B.C /1H -1B*,1H-/ »"" 

DATA SHEAfi /5BSHEAB/ 

DATA JSYES /5HJSYES/ 

NJBNC = NJKC + NHNC 

NJBNC .NE , ) GO TO 1000 
E EESULTS ON PEBHANENT UNIT FOB EVEBY STATIC ANALYSIS PEOB 

ITYPE ,LE. 2 ) GO TO 800 

NJTT = NJT * 3 
IF (JISBB .NE. JSYES) GC TO 785 
DO 780 I = 1.NJT 

IF (JST(I) .NE. 0) NJTT = NJTT + 1 
CONTINUE 
CONTINUE 

NTH = NTI + 1 

- STOBE EESULTS ON PERMANENT UNIT FOR THE LAST TIBE STEP 
IF ( JI ,10. NTH ) GO TO 800 

- STORE RESULTS ON PE 
NSTOEE = 4 
TEMP =0.0 

DO 790 I = 1.NJTT 

TEHP = TEMP + ZMASSH(I) 

- STORE EESULTS ON PERMANENT UNIT AT EACH TIME STEP OF 

- A PSEHDO-PYNAHIC PROBLEM HITH ALL ZERO MASS JOINTS 
IF ( TEMP ,LE. 1.0E-08 ) NSTOBE = 1 
IF I (JT-1) /NSTOBE+NSTOBE . IQ. JT-1 ) GC TC 800 
GO TO 1000 
CONTINUE 

BIND IWRITE 

IF (JTSHB . EQ. JSYES) GC TO 910 

HSIT DO" loo 1 ?^ \ NJT U) ' DIY(I) ' DZZ ( 1 )' 1=1, HJT ) 

NTEHF ='NSXX(I) + NSYYfl) ♦ NSZZ(I) + NSXP (I) + NSYP(I) 

IF ( NTEBE .EQ. ) GO TO 900 
HBITE(IHSIT"' 



REMANENT UNIT SVEEY 4 TH TIHE STEP. 



B 



E ) 'ilZXQ, J) .VBTXil, J) .UR-Ill.J) ,HETY(I,J) .HBZ(I,J) , 
8B|Z|I«Jl ,HBXP(I,J), SHTXP(f,jf,HRY^(l,jf ,HBfYP(i,J), 



Hiil 



CONTINUE 
GO TO 950 
CONTINUE 



,D2Z(I),DVV(I) , 1 = 1, NJT) 
"ETS(I,J) ,J=1,3) ,1=1, NJT) 



ITE (IHBITE) (DXX(I) ,DYY (I) ,D5 

( SIISI ;;«f^<f)^YY(I^NSZZa) + NSVV(I, + NSXP(I) +S SYP(I) 



IF 



mil 

10241*75 

10242*80 

10243*88 

10244*88 

10245*13 

10246*13 

10247 

10248*58 

10249 

10250 

10251 

10252 
10253 

10254 

10255 

10256 

10257 

10258 

10259 

10260 

10261 

10262 

10263 

10264 

10265 

10266 

10267 

10268 

10269 

10270 

10271 

10272 

10273 

10274 

10275 

10276 

10277 

10278 
10279 

10280 

10281 

10282 
10283 

10284 
10285 
10286 

10287 

10288*10 

10289*10 

10290*10 

10291 

10292*16 

10293*75 

10294 

10295 

10296 

10297 

10298 

10299*82 

10300*82 

10301*82 

10302*82 

10303*82 

10304 

10305 

10306 

10307 

10308 

10309 

10310 

10311 

10312 

10313 

10314 

10315 

10316 

10317 

10318 

10319*75 

10320 

10321 

10322 

10323 

10324 

10325 

10326 

10327 

10328*75 

10329*75 

10330*75 

10331*84 

10332*84 

10333*84 

10334*84 



328 



}' m ^mmmi^m.^i^» a ^- m 



we: 
1000 



i-^nn am a j 

1200 CONTINUE 



5*84 

940' CONTINUE ""' l * f-1 '■««U««»I ' J = T# 1« ) 10337*84 

950 CONTINUE 10338*84 

IF ( ITTPE .IE, 2 ) GO TO 1000 inflS?* 75 

m ~lliW» ' <"&»&&. ww» » I= WI ' illll 

HPRINT = 1 03U3 

IP9 .20- ) GO TO 1050 iXiut 

1050 c6NTiN5i 1)/ * P9 * li>9 ' EQ - JT " 1 ' HPfiINT = 1 103^ 

1100 ^N« E ' EC - HTI1 > H *™ = 1 ]j)|} 

DO 8500 JJ = 1.NH 10|51 

ISTT = IST(JJ) inlci 

MODEL! = HdDEL(ISTT) iMM 

INLOPT = INLOP ISTT) JSIfS 

ELEBNT = ELEflNjlSIlf i^ILm 

IF ( INLOPT .Eg. Y GO TO 1200 S«f 10 

CONTINUE^ = NSXL <iSTI) + NSIL(ISTT) + NSZL<ISTT) 10358 

COMMENT - SKIP gggftlM ■ffljgli 9 .M » BE AVOIDED lilff 

COBMENT - SKIP FOR COMPLETE OUTPUT™ 21 °° 18H2 

COGENT - ||I^T i g|pi i ^ B | S „ L TS {g.JJjlDWI ON 1 SHEET ]j]|| 

iS jHi&S* 4) G0 T0 150 ° iSJii 

1500 IPC = 1 10370 

1600 CONTINUE 10|71 

COtfMSM| - PRINT HEADINGS JSIl? 

PRINT 11 1 0373 

PtlHT 16, NPRCB, (AN2 (II) .11=1,9) inl?Lc B 

PHINF L" - EQ - f > G ° *° 176 ° 10°37l* 55 

1700P B INT G °^ 2100 ]8|J| 

2100 CONTINUE 10379 

COMESJ £ THE JOI»T IgglLlBHjDH CHECK AND FOR THE FINAL MEMBEB SOLUTION 10383 

IF ( ITYPE GE< 3 !AND?'liilN L E^'lV^o TO 2 150 ISIIS* 74 

IF NJNC .ST. .OR. NHNC . ST. 01 co^n? l4l * ,OU J93§9 



2150 gJggI«)"«/V l»,-1l - ™ " 7 -386 



I fS§ ^OR-gSNC^M.-g) - PB NT^7?7° " M 
?,£i JJ ) -EQ. 1) PRINT 99 
.. —Wu E 

IF ( HPBINT .HE. 1 ) GC TO 7100 \9Ml 

printMo^ ' GE ' 3 > G0 T0 220 ° ioIIo 

GO TO 2250 10391 

220u PBINT 220, JJ, JT, TIHE 12392 

llll lllll Hj^J* Hl^i 3- » 0393 

2800 PBINf 9 , f SHV3ST - EQ - S ' G ° T ° 510 ° \P¥ 

3100 PKINT td1 l J 10399 

COMMENT - PRINT COMPLETE MEMBER RESULTS \m$° 

DO 3400 A I £ ="1°BP1 10402 

SCALE = SCALE / 2.0 ?S«S§ 

DO 3800 I = 1.MP1 10407 

DO 3500 II d 41 10408 

3500 ALPHA(II)'- A 10JJ09 

ALPHA 2l[ = C 10410 

" ( BTE^I = G |l 1 - 0D -1 5 ) =° TO 3 600 }° iU 

GO TO 3650 10413 

3600 CONTINUE 10414 

3650 COKlSSl" = 1 °'° * D * (I) ' SCALE + 21 " 5 104li 

ALPHA (MTEMP) ■ B JSffH 

" ( SlS^O.'o 1 G ° T ° 365 ° 10°4]9 8 

?: v r ( i 2) io°4i° 

3M = -il'(2) 1 0< +22 

GO TO 3700 10423 

3660 CONTINUE 10424 

17 ( b^S-iTt 1 GC T0 3670 i821l 

DIS = DIS + TH 12 U27 

V = -0, D*|V2|I) - Vl(lPliJ 10U30 



329 



GO TO B h0Q = 0.5*(B2(I) - I1(IP1J, ,«„, 

3670 CONTINUE J0432 
DI5 = DIS ♦ TH IgJll 

T = U2fMP1) 10434 

V = -vi(Hp'l) 10435 

BH = »2fHPl< 10436 

3700 CONTINUE **\ nl/l l 10437 

380C PMH 2oHTifiaE IS,DJ£(1, ' DI(1, ' M(I1 ' 1 ' T » BH »< A1PHA ( II )» II=1 '41 ) 10439 

PBIslMg""" 1 ' £Q - SHEAB > G0 TC «M lS44?*10 

DO 4000 I = 2.BP1 IS 442 
4000 PBIN ?ONTlfiaE' ITS(f) ' £f,SLON(I) ' BH1S(I) ' CDHVA1 < I )' BM2S ( I ).CaRVA2(I) 10444 

GO TO 4300 10445 

4100 CONTINUE 10446*15 

PBINT 300 10447*10 

DO 4200 I = 2.HP1 10448*10 

4200 PBIN ?ONTiNul' fTS(I) ' EPS10H(I) ' BHS(I) ' CDEVAT f I )' SHS (I)'CAH H A(I) 10450*10 

4300 CONTINUE 10451*10 

GO TO 7100 10452*15 

5100 CONTINUE 10453 

COHHENT - PRINT PABTIAL HESBER RESULTS J?.^ 

TL = - D1/21 HI1S5 

VL = V172 10456 

BHL = -H1I2] 10*57 

Tfi = u2(BP1) 10458 

Kr VSi[g|{ Mil 

7100 """c'gn'tINuT (JJ) ' JT2 iL) .«.«.W.n # Btt.SM 1§2|] 

IOPL = lOPOP(ISTT) 1 7*^ 3 

if kIHI :Iq e : V""'" 1 ^" * Ea * 1 } G0 T0 7150 

7i5o ^■i!SSF E ' EQ - 1J p ™ 54 io°46 6 ^ 

7200 CONTINUE 1 0i*6 8 

IF ( NJHNC .HE . ) GO TO 8000 S!^ 

IF l ITYPE .IE. 2 )GC TO 7250 I2S 7 ,? 

IF f J| ,EQ. NTH [ GO TO 7250 Wli] 

GO I0 ^3o1)/ NSI CEE*NSTOBE . 1Q. JT-1 ) GO TO 7250 ]$$% 

7250 COBTINUE 10474 

WRITE? IWSITE) ( DX(I), Dill), DZ (I) . 1=1 BP2 > ln«?I 

if I iftSS :J8: 8 1 §8 18 Iff ' jjj»f 

7*.'" 1 «SSf " 5S «-'^' iWHff tf i-PPfiifl :»FI»i:^-, 18338 

IF f HODEIT .£,£. -1 ) GC TO 8000 1 oSI4 

" ^I^L'S 3 * SHEA ^ G ° T ° 74 °° ]o«I§*78 

IBIU(XitflXTS) (^Wy«I ,J .1) .BHJ1|1I .J ,?>,f£B25(I -J .K), , ]^85* 78 

IF ( HODEIT .lof ( 0') 'S^'lo 806S 5sia1) ' ^1,HHPtsf, 1=2, HP1 ) 10486 

SEITE (IWRITE) <<(|PBF1 /{I,J,K), EPBFT1 (I, J ,K) , SLBF1 (I.J K) 10488 

I SIBFT1 I,J,K , EP3F2 \x'j,K I EPBFT2 iIj'.K ! 10489 

GO TO 7500 1,«»PCS ), I - 2.MP1 ) 10«f 1 

7400 CONTINUE IBS!?! 7 ! 

NHINGE = 1 pu49j*78 

WRITE (IHHITE) ((( EPE1S(I,J K). EPRT IS (I, J ,K) , 10495*78 

«RITE {JSSITE) <((|PBF1 h,J,K), EPBFT1(I J,K) SLBF1 CI.J.K). 10°498*78 
7500 CONTINUE S1BFT 1 U, J, Kj , K= 1, MSSIB 1 ) . J=1 ,KNPCS) , 1=2, &P1) 10499*78 

SHITE (IiiBITEi f < ^EPSfllY/T-I-.T» pd?»t» /t t t, C r,™„„- T , ,. !9|00*78 



SHITE (IHfilTE) (<(EPSMAX(I,L,J), EPSHIN (1.1, J) , EPSPRE (I.L.J) . 10501 

\ 17 I BODELT .NE^VGoioW 1 ' * H1iSi > ' S = 2 '« P1 > gfg 2 

? WRITE (IWRITE) (C«SBO»('a.L.J,- YIGHOW (I L, J, , J = ,,„ K S ), 10504 

CONTINUE L 1 '« 8IllS S >. I - 2,«P1 ) 10505 



10502*78 
« S ITE^i«ri^r(V(IGR5w'^J)^GR0N(I L.J), J = 1,„ S p C S ), 
3000 CONTINUE 1,N3INGE J. I - 2,HP1 ) °f°J* 78 

„„„„ IF ( ITIPE .LE. 2 ) GO TO 8500 inl?,T 

COMMIT - IDSiJTIFYJLL KCNITOfi^MEHBERS AND STORE THEIR HYSTEBISIS RECORD10508 

3100 CONTINUE = 10510 

IF ( IMa(JJ) EC. ) GO TO 8200 |§|]J 

cSSKH : ip^P% I iii!SI!!.^SiJ3!S8 ft Si8Siiir THE SECII0N l§li!* 82 

IF la i*S2Lj5S:Jf4»l,l2 I j 8105 Ijj }•« 

IF ( IPIBL(iSTT) EQ. 1 i NLE = 1 18S16 

STEANL II, JT) = EPSLCN(ELE + 1) ^^n 

BQOHNL II.JT = BH1S NLE+1 lg|f? 

FORCES (II.JT) = TTSSGT inioi 

IF ( IPINK(ISTT) lEQ. 1 ) NEE = NP2 inf^u 

STRANR<II,JT) = EPSLCN(SrE-I) 1gi$g 

BaOHBB II, JT = EH2S NEE-1 -fOSSl 



330 



m M CpnS{II,«) = CURVA2(NRE-1) 10527 

GO iO 0110 10^53*39 

8105 CONTINUE 10529*0? 

IF (IPINL(ISTT) . EQ. 1) NLE = 1 10530*82 

FOBCF.L(II,JT) = TlSLEF 10531*82 

STRANL(II,JT) = EPSLGN (NLE+1) 10532*82 

BKOHNL (II, JT) = BBS (NLB+1) 10533*82 

CURVAL(II,JT) = CUEVAI(NLE+1 10534*82 

SHFO£L?II,JT = SHS (NLE+1 10535*82 

GABHALJII, JT) = GAHHA (NLE+1) 10536*82 

IF (IPINR(ISTT) . BQ. 1) NEE = 1 10537*82 

FORCER (II, JT) = T1SRGT 10538*82 

STEAM (II, JT = EPSLCN(NRE-I) 10539*82 

BBOMNE (II, JT » BHS NRE-1 10540*82 

CURVAE (II, JT) = COBVAT(NEE-I) 10541*82 

SHFOEfl(II,JT) = SHS (NBE-1) 10542*82 

GAMBAE (II, JT) = GAHHA (NRE-1) 10543*82 



8110 CONTIND 



10544*82 



S222SSS " S^S £OLi.O«ING STKNTS (OPTO #8200) STOBS THE INFCBBATION ABOOT 10545*90 

COMMENT - THE HEBBEE RESPONSE IN THE DIRECTION OF ORIGINAL GEOMETRY. 10546*90 

FBBAXF (II, JT) = -01(2) 10547*88 

FRBAXD II, JT) = DX(t) 10548*88 

FEHSHF/II^JT) = V1)2 0549*88 

FRHLTD(II,JT) = DYJli 10550*88 

FBHflOM(II,JT| = -Hf(2) 10551*88 

FRHROTJII.JT) = DZCff 10552*88 

TOAXF(2l,JT) = U2(HP i l) 0553*88 



TOAXL(II,JT) = DXJHP1) 10554*88 

T03HF II, JT = -vi(HPl) 10555*83 

TOLTE H,JT) = DY(BP1) 10556*88 

TOSOH(II,Jlf = H2 HP1 10557*88 

„„„„ TOEOT(II,JT) ■ DZ(BP1) 10558*88 

8200 CONTINOE 10559 

fci500 CONTINUE 10560 

IF ( ITYPE ,GE. 3 ) GO 10 9000 10561 

IF ] NJENC . NE - ) GO TO 9000 10562 

9000 H1 %feSSS« « "»<t.J>. *■'.«■!. *-*>* ) |gS{| 

' NJMNC .NE. ) GO TO 9900 10565 

ITYPE .IE. 2 ) GC TO 9500 10566 

JT ,EQ. NTH ) GO TO 9500 10567 

, (JT-1)/NSTCR£*NSTORE . EQ. JT-1 ) GO TO 9500 10568 

TO 9900 10569 

9500 CCSTIHOS 10570 

ENDFIL2 HRII2 10571 

BEHIND 13 10572 

WRITE(13) IWSITE 10573 

ENDFILE 13 10574 

IF ( ISHITE .EO, 12 ) GC TO 9600 10575 

IBRITE = 12 10576 

GO 10 9900 10577 

9600 CONTINUE 10578 

IWEIIE = 11 10579 

9900 CONTINUE 10580 

H2IDHN 10581 

END 10582 



******************** ************** SUBROUTINE ********************************* 

SUBROUTINE ADCYN (J1N,FSS) 10583 

COKMEHT - SUBROUTINE ADDYN, CALLED BY SUBROUTINE DYNA, ADDS THE 10584*90 

COMMENT - CONTRIBUTION DUE TO MASS AND DAMPING TO STIFFNESS HATEIX TO 10585*90 

O-.Jli'lEUT - OBTAIN INCREMENTAL JOINT DISPLACEMENT USING CONSTANT AVERAGE 10586*90 

COMMENT - ACCELERATION METHOD. 10587*90 

IMPLICIT REAL*8 (A-H,0-Z) 10588 

EEAL*4 DISJT 10589 

DIMENSION FSS(3) 10590 

COMMON /BLOC10/ SSL{4,24) 10591*79 

COSSBOH /BL0C21/ ACCJT J1Q0) .VELJT(IOO) -ZMASS R ( 1 00) ,DACCJT{100) . 10592*85 

2 DV2LJIM00) ,FACCJT (100) ,FDAHJT(10O) ,CDAMP ( 100) , DIS JT (80 ,7 1 ) 10593*88 

COMMON /BLOC23/ DFFSJ4.25) 10594*82 

COMHON/IIC/ ERE1, ERRZ.EEI, EE2 ,DTI,CS, NTI,HB (20) ,MJ(20) , BSITF, 10595*88 

2 MNITH,NSHJ.NS&M 10596*88 

DSS2=4.0/D1I**2 10597*87 

DSS12=2. 0/DTI 10598*87 

DO 100 I = 1,3 10599 

ITEMF=3*JTN-3+I 10600*87 

100 SSL <I,I)=SSL (1,1) +DSS2*ZBASSR (ITEBP) 10601*87 

2 +DSS 12*CEAMP (ITEBP) 10602*87 

DO 200 I = 1,3 10603 

200 FSS(I) = FSS(l) + DFFS(I,JTN) 10604 

RETURN 10605 

END 10606 



********************************** SUBROUTINE ********************************* 

SUBROUTINE DYSTLD (FJX , FJY,FJZ, FJV, TIME ,JTN) 10607*82 

IMPLICIT REAL*8 (A-H,0-Z) 10608 

DIMENSION 001 (300) , KW1(3C0) 10609*87 

COBI10H /BLOC1/ ZMASS(25) .FTBJXX (25) ,FTHJYY(25),FTEJZZ{25) , 10610*82 

2 FTBJVV(25) ,IT«J(25) ,!!FTXX (25) ,NFTYY (25) , NFTZZ (25) ,NFTVV(25) 1061 1*82 

COMMON /BLK7/ INLOPT, IF AE,KCFFJ,KOFFQH, KOFFSE 10612 



331 



COMfiEST - I - CUHVE 10615 

IF (NFTXX(JTN) .BO. 0) SO TO 3510 }%%]% 

NC = NFTXX(JTM) 1°6 17 

NPTT = NPTVrNCi 10618 

DO 3505 I = 1,NPTT ' 10619 

*R,is W.W = SVL(NC,I) ]0°20 

505 Il 1 <H^ »tj|kc;i |2f§l 

iJ = TIME / TTK.Jf.1Tim lUb«>2 

3510 CONTINUE 10626 

PJX=0. 10627 

3511 CONTINUE 10628 

CO H «ENT - ^-'clfvl™ - £ 2- 0) SO TO 3520 Jjgg 

NC = NFTYY(JTN) inlll 

NPTT = NPTV(NC) 10632 

DO 3515 I = 1,NPTT ' 10633 

„., 83 1R = NVL(NC,I) 10634 

515 I! 1 * 1 ! " NTJJNCI J 0635 

BJ = TIME / ITMJ(JTN) 12N 6 , 

CALL C0B«1 (QQ1 H1 f WJ HiTT.isiH.FJT.SJI.KOFPJ) } Q Hl 

GO TO 3521 fTHJYY (JTN) 1063g 

3520 CONTINUE I2ff9 

FJI = 10641 

3521 CONTINOE 10642 

COMMENT - P- ( ^fI (JTN) * E2 ' °> G0 T0 3 "0 Ititi 

HC = NFTZZ(JTN) incffl 

NPTT = NPTVfNC 122ft 6 , 

DO 3525 I = 1,NPTT ' 10647 

**■>*. Q0 -1R = NVL(HC.I) 1°6«8 

3530 CONTINOE 10654 

FJZ = 0. 10655 

3531 CONTINUE 12£f 6 

COMMENT - V- l EUl iJ ^ '* Q ' 0) G ° TC 35 "° 1 8112-82 

NC = NFTVV(JTN) 10660*11 

NPTT = NPTVfNC) 1nfifi1t(n 

DO 3535 I = 1,NPTT ' infifiU«9 

aoe 22 1 (I) = NVL(NC,I) 1oII^*fl7 

3535 HWlflj = NTJJNC'I 10664*fl? 

BJ = TIME / ITBJ(JTN) lOfittlS* 

CALL CUHVE1 (C 3 1 W«1,*J n|t! , is YM,F JV,SJV, KOFFJ) iSfftXII 

GO TO F 354l " V FTSJ " (JTt,) S!|Z:ii 

J540 CONTINUE inflllf? 

FJV =0.0 {nsTn.ii 

3541 CONTINOE }°J?°Ii3 

HETUEN !Rf4o 82 

END I U O / 2 

B * s 10673 

*****%nttnnXTZt*ruitlV* l *X%*,**^* SUBROUTINE ♦*♦*+**»*♦*******♦*********♦♦*»*♦ 

SUbfiOUTINE CUEVE1 ( QQ1, WB1. WJ. NPT. ISYM. OJ <;;> unpn i int-in 
COHSENT - SUB|00TIN| CIJR^^l|TEBE6LATSstt6lIG A 6y§AHIC FOficFguWlS 10675 

DI3EMSIOS UQl(30d)» HVI'OOO) 10677*87 

Wijti — U 1 Afi7 fl 

Go" io S Iio5 EQ - 1 ' AKD - " - LT - °- 0) G ° T ° 210 ° 0679 

2100 KJ = - klJ 10680 

2200 CONTINOE IRtoS 



3040 



3045 
3050 



DO 3040 NP = 2, NPT iHIau 

C I U^ m|IP " 3045,3055,3040 |f|| 

NP = NPT Iflfifi? 

GO TO 3050 infi«« 
IF ( ^OF^ 1 i 1 V 3050,3055,3055 

3055 NP = NP - 1 12?|? 

T ^ 2 z^mifi hi\v Q mm<r u ™* 1} - swi(hp)) mn 

IF (NIG .EQ. 0) GO TO 4300 10694 

kJ = -«j 10695 

4300 CONTINUE !2£ot 

ISS ™ 10698 

B81i 10699 



332 



***+**+***********#****•**+♦*»»**» SUBROUTINE ********* 
h SUBROUTINE CSELCT (Tfi , KEY, I.TIMETlI) 
COfiflENT^-JOBaOOTIS^CSPLCT^LOTS HONITOr' JOIST HESPOKSE 

cdanoK /gt/"hjo 



2 COBHOH/IIC/ 2£|1,ERR2 5 Efi^ES2,DTI,CB,NTI,aM(20),HJ{20),BNITF, 



DIHSNSION Tfi(71) 
1 FORMAT(1H1) 

30 F0H3AT (5X.7HJ0INT 

31 POflHAT ■ 




,1X,10 



GO TO 250 



103 F02HAT {2X,2HJT,2X,«HTiHE, 2X, 12HROTATION 
„„ 2 /„12X, 11HV-ROTATION ,//) 

104 FGE3AT (2X,2HJT,2X,4HTIHE, 2X, 1 2HSH. flOBENT (Z) , IX, 10 
* ///) 

TIM23 = TIHE - MTI * DTI 
NTH = NTI + 1 
PHI NT 1 

IF (II .SO. 1 .OH. KEY .EQ. 5) 
IF (3JO . EQ. 0) GO TO 250 
IF (flJO .EQ. 1[ GO TO 240 

BJB = flJ(II-1) 
GO TO 245 
240 MJB = MJ(1) 

245 PEINT 31.I.HJB 
GO TO 251 

250 PEINT 30,1 

251 CONTINUE 

300 PHINT°lS§ (300,400,500,600,700), KEY 

GO TO 1000 
400 tSINT 101 

GO TO 1000 
500 PRINT 102 

GO TO 1000 
600 PRINT 103 

GO TO 100 
700 EEOT 104 
1000 CALL SPLOT ( IE, 
BETUHN 
END 



(5HIXXXX) ,1HI, 
(5HIXXXX) ,181, 
(5HIXXXX) ,1HI, 
(5HIXXXX) ,1HI, 
(5HIXXXX) ,1HI, 



NTH, 1, 1, 1, NTH, TIHE3, DTI ) 



************************ 

10700 
AGAINST TIHE. 10701*90 
10702 
10703 
10704*88 
10705*88 
10706*82 
10707 
10708 
10709 
10710 
10711*88 
10712*82 
10713*88 
10714*82 
10715*88 
10716*82 
10717*88 
10718*88 
10719*88 
1072 
1072 1 
10722 
10723*88 
10724 
10725 
1072 6 
10727 
10728 
10729 
10730 
10731 
10732 
10733*88 
10734*82 
10735*82 
10736*82 
10737*82 
10738*82 
10739*82 
10740*82 
10741*88 
10742*88 
10743*82 
10744 
10745 



********************************** 



SUBROUTINE ******* 



C 

c 
c 
c 

c 
c 



10 



SUBROUTINE SPLOT (F.N .N1 , »2 ,N37n4,X ij H) 

SOB SPLOT WILI k&T A F&NCTION F(X — ALL A 
I ( m ^^ S J IiGLY SUBCBIPTED VARIABLE CONTAINING 
N = TOTAL NUMBEB OF POINTS IN F ( ) Si = 

N2 = IHCKcUENT BETWEEN PLOTTED POINTS N3 = 
H4 = LAST POINT TO BE P10TTED 11 = 

H = X DISTANCE BETSEEN POINTS IN F() 

IHPLICIT EEAL*8 (A-H,0-2) 

DIMENSION F(N), ALPHA (51) 

DATA A,B.C/iH , 1H*, 1H-/ 

FOBMAT (1H ) 

15HALL VALDES ZEEO) 



FOR 
FC 



TA A,B,C/ II 

EMAT (1H ) 

RHAT ( //>, 

2MAT { 14, 



IX, 1PE12.4, 51A1 j 



DO 



80 



85 

90 

100 
105 



10X, 
, f8.5, 
X = XI 
V = 0.0 
30 10 I = N1,N4 
Z=DABS(F (I)) 
IF (Z .Gl, V) V = Z 

VS = V / 2.5 
IF ( VS .EQ. 0.0 ) GO TC 100 
fl = 1 + (N4 - N1WN2 
90 J = 1,S " 

I = N1 + (J-1) *N2 
NF = 10.- 
DC 80 II = 1,51 

ALPHA (II) = A 
(II .EQ. 26 ) ALPHA (II) = C 
ill .EQ. NF 



.0*F(I)/VS + 26.5 



IF 
IF 

CON- 
PEINT 7, 



If ( 



N0E 
I. X. 

EN2 = 
X = X 

N3 .EQ 



B 



U Zi 



AIPHA (II) = 
( ALPHA(II) , 11=1,51 ) 



N3 1 

LL 



H*BN2 
1) GO 



DO 
PEINT 3 

CONTINUE 
GO TO 105 

PEINT 4 

CONTINUE 
RETUfiN 

END 



N3 - 1 

= 1,N31 



TO 90 



****************** j,******* 

10746 
EGDBENTS ARE INPUT 10747 
rjX) 10748 

FIBST POINT TO BE10749 
INCREMENT BETEEEH10750 
X VALUE OF FIRST 10751 
10752 
10753+87 
10754 
10755 
10756 
10757 
10758 
10759 
10760 
10761 
10762 
10763 
10764 
10765 
10766 
10767 
10768 
10769 
10770 
1C771 
10772 
10773 
10774 
10775 
10776 
10777 
10778 
10779 
10780 
10781 
10782 
10783 
10784 
10785 
10766 
10787 



333 



********************************** SUBROUTINE 

SUBROUTINE DETAMS (DELA.DELP, DEIS, I. D ,11, BH.SH) 
COHMEST - SCBfiOUTINE DETAMS COMPOTES THE AVERAGE AXIAL THRUST. BENDING 
COMMENT - MOMENT AND SHEAR FORCE IN AN DISCRETE ELEHENT. AND ALSO THE 
COMMENT - INCREHENTAL FORCE-DEF05 KATIcVm ATEIX FOR AN ELEMENT WITH 
COMMENT - LINEAfi STRESS-STRAIN CURVE (INLOP1 = 01. £L£BiB1 " ilH 

IMPLICIT R2AL*8 (A-H, O-Z) l ' 



DIMENSION D (6,6) ' 

DIMENSION E?SCOH{10), SIGCCa(lO) 



COMMON /BLOCK2/ DXS 

2 DC2S( 25) , PRF 

3 PEAGf25). ELE 

4 IOPOPj 25), IPINL 

5 NAL{ 25), NSXL 

6 NSXR( 25), NSYfif 2 
CGHMON /BLOCK4, 



% 

JT1'(50") , ' JT2l$0J', ' 
COMMON /BLOCK7/ F( 22), 
SZ( 22), Qtt 22/, 



i( 2 ^,'. 



V FOHHJ50, 



i 22], 
QX( 22) , 
*( 22), 



DY( 

S*T( 22) 

BM1S ( 22 



>Z( 22 
SQY( 22), 
?*j(_22' 

COKMON /B*ALA09/ GL { 
COMMON /BLOCK9/ BCL 



lis I 22), 



-Wit 

YCL (10) , DYCl(10f, 

depsl(iO.ii) ,issf hoi. 

ON /BALA12/ SHCJ20.10) 

COMMON /BLOC12/ SM (20,10), 

1 YI(20.10), NSS|20,1D), 

COMHON /BALA13/ GS(08) ' 

COMMON /BLOC13/ SPTST08), 



DYS 

PEA 



I?INR( 25), 
NSYL( 25' 
NSZBf 2" 
SHC(50,2 
NITM 
A2( 22)', 

C T 1 22 ir 
EBX( 22), 

SQZ 22), 



ZLS( 25) , 
QH( 25), 



. ^3 

2 5) 
2 5 

1(50 



( 22J 
J 191/ 



********************************* 

10788**9 
10789**9 
10790**9 
10791**9 
10792**9 
10793**9 
10794*13 
10795*78 
10796*42 
10797*42 
10798*42 
10799*42 
10800*42 
10801*42 
10802*31 
10803*31 
10804**9 
10805**9 
10806**9 
10807**9 
10808**9 
10809**9 



25 
25 
25 



NC51 
NSZL 
NCDS 
1ST (5 0)' 

QZ 

EH 



nnisu) , imc( 
( 22), SY( 

T( 22) , ER2( 




DC1SJ 25) , 
WH{ 25),' 

, INLOPf 25) , 
, NAB ( 25) . 
, IAXOPS( 25) 

It (50), 

IMC (50) 
■ 22 , 
22Y. 
. 22) , 
V ( 22) , 
DS(3,3, 22) , 



DGL(IO), SHCI(ID), DSHCLMO) 10810*48 

DBCLhO). DCL(IO), DDCL(IO), 10811*31 

SIG £il?', ,U' »SL(lfi.11) f DSlfiL(«.n), 08 2*31 
NSSL(10), NSSB(IO) 10813*31 



EM(20,10) , 
NA(20) , 

ISS( 8) , 

SIGT(21) 



BI(20,10), 01(20.10). 
NCDA(20), IREdT(5o,l6) 

NSIG(08,11) ,NEPS(08,11) , 

EPSTSJ11), SIGTS(11) 



2 NSITM1). NEPT/11) 

C0M30N /BLOC15/ EPST{21}. S„ 
COMMON /BLK1/ IOL, E1EMNT, NJST, KEEP3C, NC63C, 

KEEPS, KEEP3A,KEEE3E,KE£E4A,KEEP4B,K£EP4C,KEEP5A, 
B,KEEP5C,KEEP5D,KEEP6, KEEP7, NCD2. NCD3A, 



KEEP5L 

KRIS' S£S UA ' N^iiE, NCD4C, NCD5A^ NCD5B, NCD5C; 

HCD5D, NCD6. NCD7, IP8, IP9, IP10, ITYPe' 

IABAN, IPOfifi, SB. SJl' NST' NLT, H. ' 

MP1, MP2, ISTT, LTT, ITYPEL,IDj' NSTL 



COMMON /BLKV XlTxe.XI .12, ' *"' H, Ih'hSqThCU ,X2L ,11 , 12 NO 
COMMON /BLK7> IKLGpf . IFAE^ KCFFJ,KOFFQH°KOFf SE ' ' ' U 

COMMOS/ITC/ EEB| fi E|R| ER^ EE2,DTI,Cfl,Nfl,MM(20),HJ(20),HNITF, 



COMMON /SKT10/ NDIV(20.10). NPCTOT(20) 

COMMON /SKT 12/ EPSIEL(08,o3) , SIGMAX { 08 ,03) 

COKMON /SKT15/ JJ u«»i« , UJ ; 



COMMENT 
COMMENT 
COMMENT 



COMMON /SKT25/ TTSLEF, TTSRGT, 
COMMON /SKT317 ALPHA (8), BETA 
2 SLCPflDJ8), SIGULT 

IF (I .GT. 2) GO TO 1500 
SKIP FOE ALL EOT FIRST ELEHENT 



.1(8) , 



NEE 
SBLSLP(8) 
MA TEL (8) 



, EPSTHD(8) , 



10814*51 
10815*31 
10816*31 
10817*50 
10818*31 
10819*31 
10820*31 
10821*79 
10822*61 
10823*61 
10824*61 
10825*61 
10826*61 
10827*61 
10828**9 
10829*31 
10830*88 
10831*88 
10832*41 
10833*78 
10834*31 

10835*31 
10836*78 
10837*78 
10838**9 
10839**9 



COMPOTE NOMBEB CF RIGID ELEMENTS AND NOMBEE OF LINEAfi ELEHENTS1 0840**9 



AT ENDS OF MEBBESS 

NE = - IPINL (ISTT) /I 

NE = - IPINL (ISTT) - 10*NB 

NLR = 1 ♦ NE 

NLE = NLR + NE 

NB = - IPINfi (ISTT)/10 

NE = - IPIHRIISTT) - 10*NB 

NltR = BP2 - NB 

N3E = NRR - NE 
1500 COUTINOE 

IF (INLOPI ,EQ. 1) GO IC 2100 
COMMEST - COMPOTE AXIAL FCRCE, MOMENT, SHEAR FORCE AND INCREMENTAL FORCE 



COMMENT - DEFORMATION MATEIX 
DO 1600 J = 1,3 
DO 1600 K = 1,3 
1600 D(J,K) = 0.0 

0(1,1) = &E]l) 



for' 



ELEHENT WITH LINEAR ELASTIC COBVE 



D{2;2) = F(l)/tH 



COMMENT 



2100 

COHMENT 
COMMEwT 
COMMENT 
COESENT 



BM = D(2,2)*DELH 

SH = D(3,3)*DELS 
IF (I .GT. NLE .AND. I .LT. NEB) GO TO 4100 
MULTIPLY VALUES BY 10 FOB RIGID ELEMENT 

TT = 11*10.0 






0(1,1 
0(2,2 

D{3,3 
GO TO 4 100 
CONTINUE 
IF (I .GT. 



BM*10.0 
= SH*10.0 



♦ 10.0 

_, *10.0 

D(3,3J*10.0 



= 1(1,1 
= D ?,2 



10841**9 

10842**9 

10843**9 

10844**9 

10845**9 

10846**9 

10847**9 

10348**9 

10849**9 

10850**9 

10851*37 

10852**9 

10653**9 

10854**9 

10855**9 

10856**9 

10857**9 

10858**9 

10859**9 

10860**9 

10861**9 

10862**9 

10863**9 

10864**9 

10865**9 

10866**9 

10867**9 

10868**9 

10869**9 

10870**9 

10871*31 

10872*31 

10873*31 

10874*31 

10875*31 



2) GO TO 2500 

SKI2 FOE ALL BUT FIRST ELEMENT 

COMPUTE SECTION PEOPEBTIES AT MEM BEES 

FROM JOINT AND DIFFERENCE IN THESE PROPERTIES BETWEEN FBOM AND10876*31 

TO JOINTS 10877*31 

NALT = NAL(ISTT) 10878*31 

IUET = NAB (ISTT) 10879*31 

NCDA1 = NCDA(NAIT) 10880*31 

DC 2200 J = 1.HCDAT 10881*31 

BCL(J) = §I(NALT,J) 10882*31 



334 



mm = fiifsitid " YCi(J,,/fl 1:1 

NSSLT = NSSL(J) 10889*11 

NSSRI = NSSfNABT.J) 10390*48 

SHCL(J) = SSC(SAIt.J) 0891*48 

Sff"(J) = (|| C (NAfiT,J) - SHCI(J))/H 10892*48 

fc>L(J) - GS(NSiiLT) 10893*48 

BGL(J) = (GS(NSSBT) - GSfNSSLTU/K 10flqli*un 

£855181 " II SXG-EP CURVE I| KOH-tlHEAB EOT ELASTIC, THEN COBPaTE 0895*31 

COMMENT - STiiESS-STEAIN CDEVE AT HEBBEBS FBOM JOINT AND DIFFERENCE 10896*11 

COJHHSHT - IN THESE PBOPEEIIES BETHEEN FflO B AND TO JOINTS 0897*3 

COMMENT - IF SIG-EP CUBVE IS NCN-LINEAB AND INELASTIC. THEN THESE 10898*11 

COMMENT - STEPS NEED NOT BE DONE SINCE THE CDB7ES INCinDISG THE 10899*11 

COMMENT - TWO MULTIPLIERS MUST BE SAME AT THE FBO« AND TO JOINTS 10900*31 

IF ( NDIVfNALT,J) .HE. ) GO TO 2200 ouj.hi* 10901*31 

NSSBJJ) = NSS(NAST,J 0902*31 

NSSRI = NSSH(J) 0903*31 

NPTST = NPTS(NSSLT) 10904*31 

D0 2ii! s I ( £ ) i: 8 iliT ssslij J : 

iL G ^= j 'Nsic ( L s iy. N ifii65rAi?,j? ALT ' J) \mhl\ 

lfsE ( -'NFP^S^^I?HfiUtII ( # LT ' J) 10909*31 

2180 conti^I sl1j ' k{ ' t»«kM - m)'A m gjj 

2200 CONTINUE 1TQ1ui4i 

2500 CONTINUE lolltJIl 

COMMENT - (IB = 1) FOB BIGID ELEMENT inqifi*11 

COMMENT - llE = 1j_FOE LIKEAfi ELEMENT 10917*ll 

IE = § 10918*31 



IF (I .Li. NLB) IE ■ 1 10920*31 

10921*31 



IF [I ,LE. NLE) IE = 1 
IF (I . GE. NEB) IB ■ 1 
IF (I . GE. NBE) IE = 1 



10922*31 
10923*31 



ZMOL =1-2 10924*11 

ZKUL = ZMUL +0.5 10925*11 

COMMENT - COMPUTE DEF02HATICNS IN ELEMENT 10926*31 

EPA = DELA/TH 10927*31 

EPS = DELS/TH 10928*3 

CUB = DELH/TH 10929*31 

COMMENT - ZEBO ELEMENT THEUST. BENDING HOHENTS. AND STIFFNESS TEEMS 10930*31 

SSI - R-P, 10931*31 

Ihi = on 10932*31 

If] z 8-9 10933*31 

fi J Z 8/ 8 10934*31 

*21 - 0.0 10935*31 

A §1 -_0.0 10936*31 

nM i7 -*n a 10937*31 

nil'll - n*n 10933*31 

nfi'il -n n 10939*31 

gH'J] :°5° 10940*44 

COMMENT - INITIALISE THE PARAMETEfl THAI IS USED TC KEEP TRACK 10942*78 

^RSSiSS " °J^M (PRESCRIBED) SUETIVIDED PIECES AND THEIB CUMULATIVE 0943*78 

COMMENT - POSITION I APPLICABLE FCB INELASTIC CASE ONLI ) «•***«» 10944*78 

ICUMU = 10 945*78 

DO 4000 J = 1, NCDAT 10946*31 

COMMENT - COMPUTE SECTION PBOPEBT1ES AT MID-ELEMENT 10947*31 

B = BCL(J) + ZMUL+EBCLfJ) 10948*31 

DP = DCL(J) + ZMOL*DDCI(J) 10949*31 

I -JCI(J) + ZflUl*EXCL(i)' 10950*31 

NSSLI = NSSL(J) 10951*11 

NPTST = NPTS NSSLT) 0952*31 

COMMENT - COMPUTE SHEAR MODULUS AND SHEAB COEFFICIENT AT AID-ELEMENT 10953*48 

SHCOfcF = SHCL(J) + ZBUL*DSBCL(J) 10954*48 

G = GL(J) + ZflUL*DGL(J) 10955*48 

COMMENT - COMPUTE SIBESS-STHAIN CURVE AT MID-ELEHENT ONLI FOB TEE 10956*31 

COMMENT - NCN-LINEAB ELASTIC CASE. 10957*31 

COMMENT - IF II IS THE INELASTIC CASE , THEN THE SIG-EP CURVE AT 10958*78 

COMMENT - MID-ELEMENT IS THE SAME AS THAT AT THE FBOM OB TO JOINT. 10959*78 

IF ( NDIV]NALI,JJ ,EQ. ) GO TO 2590 10960*78 

NPTSM1 = NPTST - 1 10961*78 

DO 2560 K = 1,NPTSM1 10962*78 

SIGCCfl(K) = SIGHAX (NSSLT, K) * SB(NALT,J) 10963*78 

2560 CONTINUE EPSC0M ^ = EPSIEL |nSSLT, K { * B^NALT^} 10964*78 

S8SSSH : 2c d lp^i^l iSsigg g§5i!I ,s «■»««»" «» *« individual nmni 

COMMENT - NOK ALSO COMPUTE THE MAXIMUM SLOPE AT THE OBIGIN OF THE 10968*78 

COMMENT - VlfiGIS SIG-EPS CURVE FOR USE IN STRAIN BEVEBSAL CHECK CASE 10969+78 

SMSCL = Si!fNALT,J) 10970*78 

EMSCL = EMJNALT.jj 10971*78 

SIGMA = NSIG (NSSLT,2) * SMSCL 10972*78 

!?I2L = N l?fiF S >is?L* EMSCL 10973*78 

SL?KA.£ = SIGtiA / PSLON 10974*78 

SSSSInJ " ???nS T ^J?5x, S ^ LL r, SL0PE F20fi YLD PT ' EPSILON STRAIN HARDENING, 1 0975*78 
£R2£§IS " 7^2?* STRAIN HARDENING, ULTIMATE STRESS, ALPHA AND BETA FACT021 0976*78 

t-UnfltNi - (rOfi MILD dTEEL ) 10977*78 

COHHSMI - IP IT IS NOT MILD STEEL, THEN THESE VALUES HAVE BEEN 10978*78 



335 



COMMENT - P80PEBLY ASSIGNED IK SUBROUTINE SECUS. 



SMLSLF 
EPSTHD 
SIOPHD 



SHALL 
EPHD 
SLHD 
SULT 
ALP 
BET 
GO TO 39 10 
2590 CONTINUE 

DO 2600 K = 1, NPTST 

2600 



SIGULTl NSSLT 
ALPHA I'NSSLT) 
BETA (NSSLT) 



NSSLT) 
NSSLT) 
NSSLT) 



* SHSCL / EHSCL 

* EBSCL 

* SHSCL / EHSCL 

* SHSCL 



IF 
DO 



|fSTS<K) = EPSLfJ.K) * ZMUL*DEPSL(J,K) 

SIGISfKj = SIGL J,k[ + ZHUL*DSIGL ( J, K 

ISST J .EQ. 1) GO TO 2650 ' 



(ISS 
2610 



K = 1, NPTS 



2610 



2650 



EPST(K) ~= EPSTS(K) 
(K) = SIGTS(K) 



SIGT 

CONTINUE 

ISSTT = 
NPT = NPTST 

GO TO 2700 



EPST (NPTST) = EPS1SM) 
SIGTS(1) 



ST(NPTST) = 
GT (NPTST) = 
K ■ 2,NPTJ 



2675 



2700 
COMMENT 
COMMENT 
COMMENT 



comheht 



COMMENT 

COMMENT 



SI [a' 

DO 2675 K = 2, NPTST 

KB = K + NPTST - 1 

KL = KB - 2* (K - 1) 

EPST(KB) = EPSTS(K) 

EPSTfKLJ = -EPSTSjK) 

SIGT(K5) ■ SIGTS(K) 

SIGT(KL) = -SIGTS(K) 

NPT = 2* (NPTST) - 1 

ISSTT = T 
CONTINUE 

SUBDIVIDE PIPE PIECE INTO TEN EQUIVALENT RECTANGLES. (TWENTY 
EQUAL 2ADIAL SEGKENTS SITH SEGHENTS IN OPPOSITE SIDES OF Y 
AXIS COMBINED) 

NPP = 1 
IF (I2ECT(NALT,J) .EQ. 1) NPP = 10 
DO FOB EACH RECTANGLE IN PIECE 
DO 3900 IF = 1.NPP 

IF (NPP . EQ. 10) CALL PIPE (B.DP, Y,IP,NPP) 
CALL FAEJB TO COMPUTE AXIAL THRUST, BENDING HOHENT AND 
STIFFNESS TEEMS FOB CNE RECTANGLE AT LOCATION OF FIRST 
COMMENT - DISCRETE SPRING IN ELEMENT 

CALL FAEJB (TT, BH,EA, EI, AEY.ISSTT.NPT . Y, B, DP, EPA ,C0B, IB, IE, 
2 SH,GA.EPS,2LEMNT,SHCCEF,G) 

COMMEST - ACCUMULATE VALUES FOB ALL BECTANGLES 

TT1 = TT1 + TT 

BM1 = BH1 + BH 



3900 



CONTINUE 
GO TO 4000 
3910 CONTINUE 



SH1 = SHI + 
Ell = EI1 + 
AEY1 = AEY1 
AE1 = AE1 + 
AG1 = AG1 + 



SH 
EI 
+ AEY 

£A 

GA 



COMMENT 
COMMENT 



COMMENT 
COMMENT 



i^ITIAI-ISE THE FOLLOEING ADDITIONAL TEEMS USED IN THE 
INELASTIC CAS.L 

TT = 0. 

3M = 0.0 

EA = 0-0 

AEY= 0.0 

EI = 0.0 
DO FOB EACH OF THE EQUALLY SUBDIVIDED RECTANGULAR PIECES 

THEjSOGLE INPUT JIB RECTANGLE ( OB PIPE IF APPLICABLE ) 

DO 3950 IJ = 1.NJ ' 

ICUMO = ICOHU + 1 



IF ( IRECT(NALT,J) .EQ. 1 ) GO TO 3920 
COMMENT - SU5DIVIDE_THE J TH PIECE AND SUPPLY B,DP,: 



NE. 1 ) GC TO 3918 



0.5 



DDP * 0.5 



3918 Y 



1.0 ) 



DP 



. ,Y FOB EACH SUB-PIECE 
AIJ = IJ 
IF ( IJ 
ANJ = NJ 
DDP = DP / ANJ 
YC1 = Y + DP * 
DP = DDP 
YC1 - ( AIJ - 
GC TO 3930 
3920 CALL PIPE ( b, DP, Y, IJ, NJ ) 

3 930 CONTINUE ' ' 

COMMENT - IF ALPHA=EETA=0 , GO TO MASING SUBROUTINE 
M .. n « n IF i ALPHA (NSSLT) +EETA (NSSLT) .LT. 1.0D-10 ) GC TO 3935 

ggSSfti : y!el¥I!o2th b IS^eL ob Ai * fii *™*° ■ ™ « ««»«»» 

CALL DfiGSOH (SIGHIS,SIFHIS,Y,EPA.CUB,CUB2,Ifl,IE 

SIGCO" 
SMALL 
GC TO 3938 
CONTINUE 

SUBROUTINE MASING EVALUATES THE HISTOEY DEPENDENT 
STRESS AND STIFFNESS, FCB THE SUB-PIECE AT THE LOCATION 
OF BOTH THE HINGES 162, ACCCBDING TO MASING PATH 
MASING (SIGHTS, 5TF HIS, Y, EPA, CUR, CO R2, IE, IE 



CUH 



2 

3 

3935 
COMMENT 
COMMENT 

CGBtiENT 

C&.LL 



[S,SIFHIS,Y,EPA,CUE,CUB2,Ifl,IE, 
>M,EPSCOM,NPTSMl,ICUMU,I,SLPMAX, 
., EPHD, SLHD, SULT, ALP, BET ) 



3S3d 



CONTINUE 

TT = 



SIGCCM,EPSC0K,NPTSM1,ICUM0,I,SIPMAX ) 



TT 



+ SIGHIS 



10979*78 

10980*78 

10981*78 

10982*78 

10983*78 

10984*78 

10985*78 

10986*78 

10987*78 

10988*31 

10989*31 

10990*31 

10991*31 

10992*31 

10993*31 

10991**31 

10995*31 

10996*31 

10997*31 

10998*31 

10999*31 

11000*31 

11001*31 

11002*31 

11003*31 

11004*31 

11005*31 

11006*31 

11007*31 

11008*31 

11009*31 

11010*31 

11011*31 

11012*31 

11013*31 

11014*31 

11015*31 

11016*31 

11017*31 

11018*31 

11019*31 

11020*31 

11021*31 

11022*31 

11023*49 

11024*31 

11025*31 

11026*31 

11027*31 

11028*31 

11029*31 

11030*31 

11031*31 

11032*31 

11033*78 

11034*78 

11035*78 

11036*78 

11037*78 

11038*78 

11039*78 

11040*78 

11041*78 

11042*78 

11043*78 

11044*78 

11045*78 

11046*78 

11047*78 

11048*78 

11049*78 

11050*78 

11051*78 

11052*78 

11053*78 

11054*78 

11055*78 

11056*78 

11057*78 

11058*78 

11059*78 

11060*78 

11061*78 

11062*78 

11063*78 

11064*78 

11065*78 

11066*78 

11067*78 

11068*78 

11069*78 

11070*78 

11071*78 

11072*78 

11073*78 

11074*78 



336 



BH = BH + SIGHIS * 


I 


aA = EA + STFHIS 




AEY = AEY ♦ STFHIS * 


Y 


,„.„ EI = EI + STFHIS * 


I 


3950 CONTINUE 




3DP = B * EP 




TT = IT * BDP 




BH = BM *{-BDP) 




EA = EA * BDP 




AEY = AEY * BDP 




EI = EI * BDP 




GA = G*SHCCEF*BDP*NJ 




SH = GA*EPS 




TT1 = TT1 + TT 




BR 1 = BH1 + BH 




SH1 = SH1 + SH 




EI1 = EI1 + EI 




AEY1 = AEY1 + AEY 




AE1 = AE1 + EA 





* Y 



4000 
COHHENT 



COHMENT - 



4100 

coaaENT 

COMMENT 
C0M2BKT 



4120 
4150 

4160 
4200 

4260 
4300 



AG1 = AG1 +GA 

CONTINUE 

SAVE AE1 AND AG1 

A£(I) = AE1 

AG (I) = AG1 

TT = TT1 

BH = BM1 

SH — ^ H 1 

COMPUTE INCBEfiENTAL FOHCE DEFOEHATICN MATBIX FOS ELEMENT 

D i 1 , 1) = AE1/TH 

Di2,2) = EI1/TH 

D 3,3) = AG1/TH 

Di 1,2) = -AEY1/TH 

DJ2,1) = D(1,2) 
CONTINUE 

HS EE v, TT , 0F THE ^ISST 6 LAST HONLINEAE ELEMENTS, FOB LATEE 
KpBEls S AKS EECclDED IliT9 ' iiHME THE HYSTEEISIS OF HONITOE 
MNITM + 2 ) GO TC 4300 
4150 



IF 
IF 
IF 



NITM(JJ) .NE, 
INLOPT . EQ. 1 



2^« 



MP1 ) 

= IT 



NE. 

TTSLEF 
GO TO 4300 
CONTINUE 
IF ( I .NE. 

TT3BGT 
GO TO 4300 
CONTINUE 
IF ( IPINL(ISTT) 

IF ( I . NE. 

TTSLEF 
GO TO 4300 
CONTINUE 
IF ( I . NE. NLE + 

TTSLEF = TT 
GO TO 4300 
CONTINUE 
IF ( IPINB(ISTT) .NE. 



) GO TO 
TO 4 120 



GO TO 4300 



Ik 



.NE. 
GO TO 



1 ) GO TO 4 160 
4200 



1 ) GO TO 4200 



BET 
END 



IF I .NE." 
IT S3 G I 

GO TO 430C 

CONTINUE 

IF ( I .NE. 
TTSEGT 

CONTINUE 
UEN 



HP1 ) 
= TT 



N3E - 
= II 



)G< 



GO TO 4300 



1 ) GC TO 4300 



11075*78 

11076*78 

11077*78 

11078*78 

11079*78 

11080*78 

11081*78 

11082*78 

11083*78 

11084*78 

11085*78 

11086*78 

11087*78 

11088*78 

11089*78 

11090*78 

11091*78 

11092*78 

11093*78 

11094*78 

11095*31 

11096*31 

11097*31 

11098*31 

11099*31 

11100*46 

11101*46 

11102*31 

11103*31 

11104*31 

11105*31 

11106*31 

11107*31 

11108**9 

11109*31 

11110*31 

11111*31 

11112*31 

11113*31 

11114*31 

11115*31 

11116*31 

11117*31 

11118*31 

11119*31 

11120*31 

11121*31 

11122*31 

11123*31 
11124*31 
11125*31 
11126*31 
11127*31 
11123*31 
11129*31 
11130*31 
11131*31 
11132*31 
11133*31 
11134*31 
11135*31 
11136*31 
11137*31 
11133*31 
1 1 139**9 
1 1140**9 



SUBROUTINE 
COHSEST - SUBBOUT 
COHHENT - KATBIX 
IMPLICIT BE 
DIMENSION a 
DIMENSION S 

2 FHM(3) ,FH3 

3 TKDT(4,4) , 
CO a HON /BLO 

2 QZZ{25) 

3 DYY(25[ 

4 EBXX(2S 

5 U3XXJ25 

6 NSY?(25 
COMMON /BAL 

2 HVV{25) 
COMMON /BLO 

2 OC2S ( 2 

3 PRAG (25 

4 IOPO?( 

5 NAL( 25 

6 NSXBf 2 
COMMON /BAL 

2 THKJ (25 
COMMON /BLC 



****************** s 
FSUB23 ( BH. BO, L6, 
IHE FSUB23 FUBNISHES 
EH AND LOAD MATBIX B 
AL*8 ]A-ii,0-Z) 
H (16, L4) t fi0(L6^ 



UBBOUTINE ************************* 
L4, IBB 1 

BIGHT SIDE OF SYMHETEIC STIFFNESS 
FOS THE JOINT SHEAE OPTION CASE 



Ma(3'37,SHS]3,3) .DC ( 3,3} .DCT (3.3) ,T33(3,3) , 



ckV i (2^1 « 

SXX(25) , 
DZZ (25), 
EBYY(25j 

;] 2 i 



NSYIl^..,,, 
ISIJS (25) 



*I 2 
SYY 

BXI 

EfiZ 

NSZ 



it iJiun i 

A01/ QVVJ25) 



CK2/ 

V' 
25), 



NSVV(2 
DXS ( 25 

?EF( 25 

HIE' 

IPIN 

NSXL 

NSYE 



25 lr 
B 251, 

L 15J , 



SVV 



DY3 

PBA 



Z(25J; 
(25) , 




DVV(25) , 

ZLS( 25) , 
QH( 25) , 



(251 ,NJ 
) ,GJ (25) ,SJt(25 
CK3/ QXL( 25) , ' DYL 



V11J1 i.\ 
JST(25l 
"• ,SJC"(25) 



IPINB( 25) , KC51 ( 25 

NSY 

NSZ 
JSS(25 



L( 2 5) , NSZL( 25 , NAB( 25) , 
E( 25), NCDS( 25 . IAXOPSf 25) 
) ,HLJ(25),HBJ(2 5) ,VLJ (25) ,VUJ(25) , 



QYY(25) , 
DXX 25 , 
EZZ(25) , 
WHJ 25[ . 
NSXP(25) , 

EE7Y(25) , 

DC1S( 25), 
«H( 25) , 

INLOPf 25) , 



( 25) 



ZLL{ 25) , DC1L( 25) , 



******** 
11 141*75 
11142*75 
11143*75 
11144*75 
11145*75 
11146*75 
11147*75 
11148*75 
11149*75 
11 150*75 
11151*75 
11152*75 
11153*75 
11154*75 
11155*75 
11156*75 
11157*75 
11158*75 
11159*75 
11160*75 
11161*75 
11162*75 
11163*79 
11164*80 
1 1165*75 



337 



JQY( 25), NCDL( 25), IAXOPI ( 25), 



COa«0| /BLOCK4/ fCBH(5p,S),SMC(50,21) ,IST(50), 11(50), 

COBaOK /BLK1/ TOL, ELEHUT, HJSI, K EEP3C, NCD3C, 

^ KE&P2, KEEP3A,K£EP3B,KEEP4A.K£EP4B.KEEP4C KFFP54 

3 KEEP5E,KEEP5C,KEEP5E,'kEEP6, MeP7,NCD2. 'fcD3A ' 

5 SSSfe* SSR2 4 ' S B ' ?CD4C HCD5A NCD5B, NCD5C,' 

? NCD5D, NCD6, NCD7, I?8, IP9 . IP10 TTYPF 

I IABAN, IFOBH, HS, VJl' "**' •"-' ? TYPE » 

7 ap1. BP2. ISTT, LTT* 

cgaaoN /blkS/ nfsu6,nitf,n1,n2 

COMMON / HI / St, BI, J1 

COMBON /HIT/ APROB 

^COaMON /SKT14 / IHV(21,2,10), 
<£ IRVRSE, ITAPE 



NST, NIT,' 
ITYPEL,IDJ, 



H$TL 



FCMCLD{50,6), 
N3 



initior., ii'APE, N3 .... 

FObSat ^PMrtMn^tW 25 * *EBYYOL(25),ERZZ0L<25) ,EflVVOL(25) 



4750 FOBHAT ( U, 10MPE13.5) ) 
DATA PRINT /4HBINT/ 



NL4 = NL 
HL4 = BL 
DO 8000 JTN=1,NJT 



COHSENT 



UU OUUU J'J.M= I ,NJT 

IF (JTN .BE. 1 ) GO TO 1300 
- SET CONSTANTS OH FIKST CALI 



J1 = 1 

IHBP1 = IHB ♦ 



FHOH GHIP2A 



1 



IHB1 = IflB - 1 
IHB2 = IHB1 - 1 
= 0.0 



DC 1,3, 
DC (2, 3 =0.0 
DC 1,3,1) = 0.0 
DCJ3,2[ = 0.0 
DCT(1,3l = 0.0 
DCT (2, 3} =0.0 
DCT (3,1) =0.0 
DCT(3,2) =0.0 
DC 13,3) = 1.0 
,,„„ DCT(3,3) = 1.0 

1300 CONTINUE 

CQKHESI - ZERO SSL AND FSS 
DC 1400 1=1,4 

FSsTl) = 0.0 
DO 1400 J = 1,IHBP1 
'400 SSL(I.J) = 0.0 

COgafiiT - DO FOE EAC& 3EHBEE - ADD ITS STIFFNESS MATRIX AND LOAD MATRTV 
COBKENT - JgTOgSJBOCIUHE^TIFFHESS BATBIX SSI AND LOAD BATBIX FSS * 



IF 

COSMENT - SKIP 

IF ( 

COBflENT - FOBH 



( JT1 (J J) .HE. J5 
l ISTT = 1ST (jjl 

FOE NOLL BEBBEB 

ISTT .EQ. 1 GO TC 3500 

incr 



JTN .AND. JT2(JJ) .HE. JTH ) GO TO 3500 



TBANSFOBHAIICN BATBIX AND ITS TBANSPOSE 
DC(1, 1) = DC 1S (ISTT) 
= DC2S(ISTT) 
- DC 1,2) 



COMMENT 



CALL 



IF 

IF 

IF 

FOB 

IF 

IF 



DC 1,2 
DC (2,1 
DC (2,2, 
DCT(1, 1 
DCT (1,2 
DCT (2, 1 
DCT (2,2 



= E ?i1cl{ 



»e f,. 

= DC (2,1 
= DC(1,2 
= DC(2,2 



DABS(DCISIISTT) 1 .GI. 0.99) KEYDET 
DABS (EC1S (ISTT) [ .LE. 0.99 KEYDET 
JT2(JJ) ,£Q. JIN 1 GO TO 2300 



T=1 
2 



_ SHU FOB SEHBEB WITH FBOH JOINT AT JOINT JTN 
(KEYDET .EQ. 1) KEY=1 
(KEYSET .EQ- 2 KEY=3 

TENSFB (KEY, JTN, TED, ID1,: 

SUM (1,11 = SHC(JJ,1) 

SBa(l,2J = SHC(JJ,2 

SaH 1,3) = sacrjj'3'i 



,ID2) 



SMB I 2, 1j 

saa i'2,2) 
saa i 2,3} 



combent 
2250 



2300 
C03.1ENT 



sac i 1 j j, 2 

SHCi JJ,7' 
SMCi JJ,8 



CALL 



SKfi 

sua 

SHfl 

FOBB FKM 

paa 

FMM 

paa 

GO TO 25 
CONTINUE 
F03H SHH FOB MEBBEH SITE 
IF [KEYDET -EQ. 1) KSY=2 
IF (KEYDET .EQ. 21 KEY=4 
KEY 



= SMCiJJ,3 
■ SfiC|JJ,8[ 

= sacljj, 121 



j, 2 

3, 3; = sen. ijo, iz) 

FOB HEBBEB WITH FROM JOINT AT JOINT JTN 

' = Foaa(jj,i) 
= fohb(jj,2 

= Foaa(jj,3 



TO JOINT AT JOINT JTN 



sa« 

saa 

SMH 

saa 
saa 
sm 

saa 



TRNSFM 



(KEY,JTN,TBD,ID1,ID2) 

1. 1) = sac (jj, 16) 

1.2) = SHC(JJ, 17 
1,31 = SMC (JJ, 18 

2.1) = SMC (JJ, 17 

2.2) = SMC (JJ, 19 

2.3) = SMC(JJ,20 
.. .3, 1) = SKC JJ, 18 

saa (3,2) = sac(jj,20 

Saa (3,3) = SBC (JJ,21 



11168*75 

11169*75 

11170*75 

11171*79 

11172*75 

11173*75 

11174*75 

11175*75 

11176*75 

11177*75 

11178*75 

11179*75 

11180*75 

11181*75 

11 182*75 

11183*75 

11184*75 

11185*75 

11186*75 

11187*75 

11188*75 

11189*75 

11190*75 

11191*75 

11192*75 

11193*75 

11194*75 

11195*75 

11196*75 

11197*75 

11198*75 

11199*75 

11200*75 

11201*75 

11202*75 

11203*75 

11204*75 

11205*75 

11206*75 

11207*75 

11208*75 

11209*75 

11210*75 

11211*75 

11212*75 

11213*75 



14*75 
15*75 



11 

11 

11216+75 

11217*75 

11218*75 

11219*75 

11220*75 

11221*75 

11222*75 

11223*75 

11224*75 

11225*75 

11226*75 

11227*75 

11228*75 

11229*75 

11230*75 

11231*75 

11232*75 

11233*75 

11234*75 

11235*75 

11236*75 

11237*75 

11238*75 

11239*75 

11240*75 

11241*75 

11242*75 

1 1243*75 

11244*75 

11245*75 

11246*75 

11247*75 

11248*75 

11249*75 

11250*75 

11251*75 

11252*75 

11253*75 

11254*75 

11255*75 

11256*75 

11257*75 

11258*75 

11259*75 

11260*75 

11261*75 



338 



FOR 



CQ8HEWT - FORK FHH 
2350 faa 

FBB 
PHH 
2500 CONTINUE 
COMEEST - TRANSFORM 
CALL HAT333 
„„ CALL MATH 33 
2550 CALL HATH31 
COBBENT - TRANSFOE 
COMMENT- SBS4 AKD 

DO 2560 . 

DO 2560 J = 1,3 



KEEBER BITH 
FONM(JJ,4 
FOHM (JJ,5 
FOMM(JJ,6 



SHM AND FMM TC 
DCT, SMB. T33 
T33, DC, SHS 
DCT, FBH, FBS 
. 3-DEGSEE OF F 
FSS4 

i«J#3 



L 



TO JOINT AT JOINT JTN 



STEUCTDRE COORDINATES SHS AND FBS 



EDOH SHS AND FHS INTO 4-DF.GREE 



2560 



CCMtlENT 
COMMENT 



2600 
COMMENT 



comae si 



CALL 
CALL 
CALL 
CALL 



SMS 3(1", J) 
ANSP 



= SMS(I.J) 
(TBD t TRDT,ID1,ID2) 



CALL 



UULT (XRDT,SMS3,T43,lD2,LD1,ID1) 

MULT JT43,TRD,sfis4,±D2.iD1.iD2) 

aULT JTEDT,FBS,FBS4,ID2\lD^,1) 
ADD (SUBTRACT) IN FHS4 10 S1EUCTUBE LOAD MATRIX FSS 
££ D oIL S $ S '} TO DIAGONAL SOBflATEIX OF SSL - SYMHETHICAL TERMS 
uu iOUU X— \ 9 xu 4. 

D O2 60 ? a S i= I I,IDl SS(I) " rHS4(I) 
co K tiI^ (I ' J} " S "< I ' J > * s B s M i,J) 

SKIP FOE SMM HEICH ARE 10 LEFT OF DIAGONAL 

JI ( JTN .GE. JT1 (JJ1 .AND. JTN . GE. JT2(JJ) ) 

IF ( JT2{JJ) .EQ, JTN ) GO TO 2700 

FORM SHt FOE MEMBER WITH FROM JOINT AT JOINT JTN 
IF (K2YDET .EQ. 1) KEY=2 
IF (K2IDET .EQ. 2) KEI = 4 
JTNT = JIT 
TRNSFH 



GO TO 3500 



2700 

comment 



SHB 

saa 

SHH 

saa 
saa 
saa 
saa 

SfiM 

saa 

GO 
CONTINOE 
FORM SME 



1,1] 

, 1 ' 3 ! 

2,1 

1*3 

3'2 

3 ' 3 

!C 3 



2 J J) 

(KEY, JTNT ,TBO,ID1,ID3) 
= SMC (J J, 4) 



SMC 
SHC 

sac 

SHC 

= sac 
= sac 

= SMC 

= sac 

oo 



;jj;5 

J J, 6 
JJ,9J 

jj,10 
JJ,11 

J J, 13 
JJ,14 
JJ,15 



IF 
IF 



FOE 



(KEYDE1 

(KEIDET 

JTNI 



fiEKBEB WITH 
EQ. 1) KEY=1 
EQ. 2) KEY=3 
JT1 (JJ) 



TO JOINT AT JOINT JTN 



CALL 



TENSFM 
SBM(1, 1) 



iK fMM E0 ' ID1 ' ID3) 

J J, 9[ 
JJ,13) 



3MB(1,2) = SBC 

saa (1,3) = sac 
sti& (2, 1) = sac 
saa \2,2\ = sac 

SBB(2,3' = SMC 

sem(3,i i = sac 
saa?3,2' = sac 
saa (3, 3 = sac 

3000 CONTINUE 

COMKKT - TRANSFORM SBM 

CALL BA1H33 

CALL HATM33 

DO 3010 1=1,3 

DO 3010 J-1,3 

sas3 (i, J) =sas(i,.Ji 

CALL BULT (TRCT,SKS3,T43,ID2.ID1,ID1) 
CALL H01I T43,iBO,SMS4 r fD2,iD1,iD3) 
PLACE 3ES IN SSZ * 

JTL = JT2(JJ) 
= JTIjJJ) 

. GT. JTS) GO TO 3 100 
= JT1 (JJ) 
= JT2 (JJ) 



JJ, 10) 
JJ,14) 
J J, 6) 
JJ,11) 
JJ,15) 

TC STRUCTURE COOEDINATES 
( DCI, SBM, T33 ) 
( T33, DC, SHS ) 



SMS 



301 



COMKEN1 



3100 



3150 



3200 
3500 

ccaaE«T 

COMMENT 
CCHHENI 

CALL 
CGBHENT - ADD 



JTS 
IF (JTL 

JTL 

JTS 
CONTINOE 

J21 



JTL -JTS 

JTLB1 = JTL -1 

ISTP = 3*J21 + 1 
DO 3 150 I = JTS.JTLM1 
IF (JST(I) .BE. 0) ISTP=ISTP + 1 
CONTINUE 
DO 3200 1=1, ID2 
DO 3200 J=1.ID3 

SSL(I,ISTP+J-1) = SMS4(I,J) 
CONTINUE 
CONTINUE 

CALL INELST TO FIND SPRING RESISTIVE FORCES AND TANGENT 
NESSES - SPRING FORCES ARE ADDED INTO LOAD MATEII ONLY 
rx^ST ITERATION FROM A ZERO DISPLACEMENT START 

s ^f^ T L ^Ss' SJX ' SJY ' 5JZ ' SJV ' SJXI ' QJX ' QJ5: ' QJZ ' QJ7) 



STIFF 
ON 



IF 

IF 



(JST (JTN 



3550 



(GITF 

QJX 

QJY 

iJZ 

CONTINUE 



= 0, 
= 0. 



) .NE. 0) 
Q. 1 . AND 

0.0 



GC TO 5500 
ITYPE . EQ. 



1) GO TC 3550 



11262*75 

11263*75 

11264*75 

11265*75 

11266*75 

11267*75 

11268*75 

11269*75 

11270*75 

11271*75 

11272*75 

11273*75 

11274*75 

11275*75 

11276*75 

11277*75 

11278*75 

11279*75 

11280*75 

11281*75 

11282*75 

11283*75 

11284*75 

11285*75 

11286*75 

11287*75 

11288*75 

11289*75 

11290*75 

11291*75 

11292*75 

11293*75 

11294*75 

11295*75 

11296*75 

11297*75 

11298*75 

11299*75 

11300*75 

11301*75 

11302*75 

11303*75 

11304*75 

11305*75 

11306*75 

11307*75 

11308*75 

11309*75 

11310*75 

11311*75 

11312*75 

11313*75 

11314*75 

11315*75 

11316*75 

11317*75 

11318*75 

11319*75 

11320*75 

11321*75 

11322*75 

11323*75 

11324*75 

11325*75 

11326*75 

11327*75 

11328*75 

11329*75 

11330*75 

11331*75 

11332*75 

11333*75 

11334*75 

11335*75 

11336*75 

11337*75 

11338*75 

11339*75 

11340*75 

11341*75 

11342*75 

11343*75 

11344*75 

11345*75 

11346*75 

11347*75 

11348*75 

11349*75 

11350*75 

11351*75 

11352*75 

1 1353*75 

11354*75 

11355*75 

11356*75 

11357*75 



339 



IF ( IHVESE .81. 1 GO TO 3580 iimR*7«; 

COMMENT - STOEE FOB USE IF REVERSAL OCCUBS LATER 11359*75 

ERXXCL(JIN) = ERXX (JIN) 11360*75 

EEYYCL(JTN) = ERYY (JTN) 11361*75 

GOTO^S 1 *™ " EHZZ * J "> }}llk}l 

3580 CONTINUE 11364*75 

ESXX (JTN) = ERXXCL(JTN) 11365*75 

ERYY JTNJ = EEYYCL JTN 11366*75 

,... EEZZ (JTN) = ERZZCLfJTN 11367*75 

3590 CONTINUE V ' 1136fi*7S 

FSS(1) = FSS (11 + EBXX(JTN) + QJX 11369*75 

FSS(2i = FSS 21 + EBYY{J1S + QJY 370*75 

FSS (3) = FSS (31 + ERZZ(JTN) + QJZ 11371*75 

COMMENT - ADD IN JOINT RESTRAINTS l ' U 11372*75 

HHM) - 2&fJ'3) + SXX(JTN) + SJX 11373*75 



SSLM,2i = SSI 1,2 ♦ SJXY 1 1374*75 

SSL 2,2) = SSL 12, 2) + SYY(JTN) + SJY 11375*75 

SSL(3,3f =SSI3 3 + SZzjjTNJ + SJZ 1 376*75 

™ ul . „ m IF i ITI P£ -GE. 3) CALL ADDYH2(JTN,FSS) 11377*82 

r.°«3£2? " n¥Ur SSL T0 FACILITATE OBTAININg'sU FBCH 2ND AND 3BD ROB 11378*75 

DO 3600 I = 1..IHB ii3ftn*7* 

"00 SSL(2,I) = SSL(2, 1+1) IlillJ?! 

,„ nn DO 3700 V = 1,IHB1 l ' ' 11382*75 

3700 SSL(3,I) = SSL(3,I + 2) 11383*75 

SSL|2,IHBP1) = 0.0 ' 11384*75 

SSL(3,IHBP1J =0.0 11385*75 

SSL(3/IHB) = 0.0 113flfi*75 

4000 CONTINUE . 113P7*7S 

DO 4500 11=1,3 11388*75 

IF(SSL(II,1) .NE. 0.0) GO TO 4500 11389*75 

COMMENT - ZERO 01* DIAGONAL MATRIX - DISPLACEMENT UNDEFINED - SET 11390*75 

COMMENT - DISPLACEMENT EQUAL TO 1.0E40 uaucriAEU bei lljyo*75 

IIHiJf 1 ) =, kJL 11392*75 

,.,-,„ FSS (II) = 1.0E40 11393*7S 

4500 CONTINUE 1139U*7? 

IF (APHOB .NE. PRINT) GC TO 5000 11395*75 

?-S2i)5MS " P?S£ CF STRUCTURE STIFFNESS AND LOAD MATRIX, TO ACTIVATE SET 11396*75 

COMMENT - LAST FIVE COLUMNS IN PROBLEM NUMBER CAHD EQ&AL TO PRINT 11397*75 

DO 4700 11=1,3 11398*75 

4700 C^NtInuF ' ^L(II,I),I=1,i aB P1,,FSS(II> |li*jf 

5000 CONTINUE 11401*75 

J1P1 = J1 ♦ 1 11402*75 

J1P2 = J1 + 2 11403*75 

IF (ML .EG. -1) GO TO 5200 11404*75 

DO 5100 J2=1,IHBP1 11405*75 

RMijl?'i 2 U2) - llifl'ji] 11406*75 

5100 CO.TlSSi* 1 "^ " SS1 * 3 ^ JjgB 

H0fj1P2l - *SS{3j 11412*75 

J1-J1 + 3 1101 1*75 

__ GO TO 8000 1 414*75 

5500 CONTINUE 11415*75 

IF (NITF .20. 1 .AND. ITYPE .EQ. 1) GO TO 5550 11416*75 

SH! - no 11417*75 

fill - n'n 11418*75 

Q«| " 0.0 11419*75 

cm** '* J ' °«° 11420*75 

5550 CONTINUE 11421*75 

COMMENT - CALL SUBROUTINE DJSTSM TO OBIAIN JOINT TANGENT STIFFNESS 11422*80 

CALL DJSTSM (JTN ,STF J ,SHMOJ) 11423*80 

IF ( IKVSS2 .NE. ) GC TO 5580 1 424*75 

CCM5EHT - STOEE FOE USE IF REVERSAL OCCURS LATER 11425*75 

EEXXOL(JTN) = ERXX (JTN) 11426*75 

ERYYCL JTN) = EHYY JTN) 11427*75 

ERZZCL(JTN) = E2ZZ JTN 11428*75 

ESVVCL JTN) = EEVV (JTN 11429*75 

GO TO 5590 V ' 1430*75 

5580 CONTINUE 11431*75 

- EEXXOL (JTN) 1 1432*75 

ESYYCL JTN 11433*75 

ERZZCL(JTN) 11434*75 

£2VVCL{JTN 11435*75 

5a90 CONTINUE 11436*75 

♦ ERXX(JTN) + QJX 11437*75 

+ ERYY (JIN + QJY 11438*75 

+ EfiZZ(JTN) + QJZ 11439*75 

+ ERVV(JTN) + QJV 11440*75 

CGflilEHT - ADD IN JCJINT RESTRAINTS 11441*75 

*(1,1) + SXX(JTN) + SJX 11442*75 

(1.2) + SJXY 11443*75 
(2,2 + SYY(JTN) + SJY 11444*75 

(3.3) + SZZ(JTN) t SJZ 11445*75 
_ „ • J • J >'^-'l.-'L ~ -J-Ji-{4,4) + SVV(JTN) + SJV 11446*75 

COMilENT - ADD JOINT STIFFNESS TEEMS \\Vn*l\ 

= SS1(Z e 3) + STFJ 11448*80 

= SSL 3,4 - STFJ 11449*80 

, = SSL(4,4) + STFJ 11450*80 

IF (ITYPE . GS. 3) CALL XdDY N2 ( JTN , FSS) 11451*82 
rKSSSSf* " f^^^^ic'? FACILITATE OBTAINING EC FROM 2ND, 3RD AND 4TH 11452*90 

LOl-IuiM - BUSS OF oSL. 11453*90 




340 



5600 
5700 
5800 



DO 



COMMENT 
COMMENT 

6500 

COMMENT 
COMMENT 



6700 
7000 



7100 

7200 



8000 



SET 
END 



DO 
If( 

DI 



CON 

IF 

DOB 

LAS 

DO 

Pfil 

CON 

COS 



IF 

DO 



CON 



GO 
CON 
URN 



5o00 
SSL( 
DO 5 
SSL( 
DO 5 
SSL( 
SSL 
SSI- 
SSL 
SSL 
SSL i 
SSLi 
6500' 1 
SSL(II 
u OH D 
PLACEM 
S3L( 
FSS ( 
TINUE 
(APROB 
P OF S 
T FIVE 
6700 I 
NT 475 
TINUE 
TINUE 
J1P1 
J1P2 
J1P3 
(ML .E 
7100 J 
RK(J 
E«(J 
RM(J 
RM (J 
TINUE 
BO (J 
BO (J 
BO (J 
BO (J 
J1 = 
TO 800 
TINUE 



M) 1 

700 I 

800 I 

4 ' X } 
2.IHB 
3,IHB 
3,IHB 
4,IHB 
4, IBB 
4,IHB 
I* 1 , 4 

.1) ■ 

IAGON 
EST E 
11,1) 
II) = 



,IHB 

= SSL(2,I+1) 

■1.IHB1 
SSL(3-I+2) 

= 1.XHB2 
= SSL(4,I+3) 
PI) =0-0 



lit; 
IK 



t* 



0.0 
0.0 
0.0 
0.0 
0.0 



HE. 0.0) GO TO 6500 

AL MATRIX - DISPLACEMENT UNDEFINED 

QUAL TO 1.0E40 

= 1.0 

1. 0E40 



SET 



. NE. PRINT) GO TO 7000 
TEUCTOHE STIFFNESS AND LOAD MATRIX, TC ACTIVATE SET 
COLOBNS IN PBOBLEB NUHBEfi CABD EC.UAI TO PRINT 

0, '(SSL(II,I) ,I=1,IHBP1) , FSS (II) 

= J1 + 1 
= J1 + 2 

■ J1 + 3 
Q. -1) GO TO 7200 
2=1,IHBP1 

1,J2) = SSL(1,J2) 

1P1,J2) = SSL(2,J2) 
1P2,J2J = SSL(3,J2) 
1P3,J2) = SSL(4,J2) 



1P2) 
1P3) 
J1 




= FSS 
= FSS 
= FSS 
= FSS 

► 4 



1455*31 
11456*75 
11457*75 
11458*75 
11459*75 
11460*75 
11461*75 
11462*75 
11463*75 
11464*75 
11465*75 
11466*75 
11467*75 
11468*75 
11469*75 
11470*75 
11471*75 
11472*75 
11473*75 
11474*75 
11475*75 
11476*75 
11477*75 
11478*75 
11479*75 
11480*75 
11481*75 
11482*75 
11483*75 
11484*75 
11485*75 
11486*75 
11487*75 
1 1488*75 
11489*75 
11490*75 
11491*75 
11492*75 
11493*75 
11494*75 
11495*75 
11496*75 
11497*75 
11498*75 



*****%ZZZZZZZZZ ZZZZZ************* SUBROUTINE ************************ 

SUBROUTINE TBNSFH (KEY, JTN. THK.IE 1 , ID2) 
COMMENT - SUBROUTINE TRNSFB PROVIDES THE SATEIX THAT TRANSFORMS HEHBEB 
C0H4ES1 - STIFFNESS AND LOAD MAIBICES IN 3-DEGEBE STR0CT0H2 COORDINATES 
COMMENT - TO 4-DEGSEE STRUCTURE COORDINATE SYSTEH JiIVU '- iun - ^ ufl "i»^" 

IMPLICIT BEAL*8 (A-H, O-Z) 



DIMENSION TBM(4,4) 
COMMON /3LOCKT/ 2(25), 
SXX(2 5 



QZZ(25) 

dyy i ' 

EBXi 
KSXX{25) 




DZZ i 
EBX1 

HSYXJ255 



U *&i>. 



m, 

-.X 25 

6 NSYP(25 . ISTjS(25f 

COMMON /BALA01/ QVV(25), 
2 SSV VJ25) " 

CCdHON /SKT2J/ PDELTA 



Six (25) , 
BXX?25[ , 

EBZZ(25J, 
NSZZ(25) , 

SVV(25) , 



QXX{25) , 
SZZ25i, 

EYY '25 
QMJ 25< 
IMJ(25 

DVV(25) , 



QIY(25) , 
DXX(25J , 
RZZ(25) , 
«flj|25J.; 
NSXP(25) , 

£RVV(25), 



IF 



DATA PDNO /4HPDNO/, PDN/4H PDN/ 
JSTT = JST(JTN) 
ID1 = 3 

0) GO TO 



700 



200 



300 
COMMENT 



400 
COMMEi 



500 
COMMENT 



600 

COMMENT 



= 0.0 



PDNO .AND. PDELTA -NE. PDN) GO TO 1000 



(JSTT .EC. 

ID 2 = 4 
DO 200 1=1,3 
DO 200 J=1,4 

TEM (I.J) 
CONTINUE 

TBM(1, 1) =1.0 

THM(2,2 =1.0 
XF ( PDELT A NE 
GO TO (300, 400^500; t>00J",KEY" 
CONTINUE 
HORIZONTAL BEMBEB KITH JOINT ON THE LEFT 

TfiH (2, 3) = HHJ (JSTT) 

TRMf3,4) =1.0 
GO TO 2000 
CONTINUE 
HORIZONTAL MEMBER KITH JOINT CN THE SIGHT 

TEM(2,3) = -HLJ(JSIT) 

TRMJ3,4) =1.0 
GO TO 20GO 
CONTINUE 
VERTICL HEHBEB KITH JOINT ON THE BOTTOM 

TRM (1,4) = -VUJ(JSTT) 

TSm]3,3) =1.0 
GO TO 20C0 
CONTINUE 
VERTICAL MEMBER KITH JOINT CN THE TOP 



********* 
11499*75 
11500*75 
11501*75 
11502*75 
11503*75 
11504*75 
11505*76 
11506*76 
11507*76 
11508*76 
1150 9*76 
1 1510*76 
11511*76 
11512*76 
11513*79 
11514*80 
11515*76 
11516*76 
11517*75 
11518*75 
11519*75 
11520*75 
11521*75 
11522*75 
11523*75 
11524*75 
11525*75 
11526+75 
11527*76 
1 1528*75 
11529*75 
11530*75 
11531*75 
11532*75 
11533*76 
11534*75 
1153 5*75 
11536*75 
11537*75 
11538*76 
1153 9*75 
1 1540*75 
11541*75 
1 1542*75 
11543*76 
11544*75 
11545*75 



341 



700 



800 

900 

1000 

1300 
CO HUE NT 



1400 

COMMENT 



1500 

COMMENT - 



H1&3) ZW** 

GO TO 2000 
CONTINUE 

ID 2 = 3 
DO 800 1=1,3 
DO 800 J=1,3 

TRM(I,J) =0.0 
CONTINUE 
DO 900 1=1,3 

Taa(i,i) =1.0 

CONTINUE 

GO TC 2000 

CONTINUE 

GOTO (1300,1400, 1500,1600) , KEY 

CONTINUE 



1600 

COHHENT 



HORIZONTAL MEMBER BITH JOINT ON T BE LEFT 
= "5HJ(JSTT) *D5IN jDZZ (JTN1) 



HBJ (JSTTJ *ECOS 



ISA (1,3 

TRM(2#3 

TRW (3,4) = 1.0 
GO TO 2000 
CONTINUE 
HORIZONTAL MEMBER WITH JOINT ON 

TEM(1,3) = HLJ(JSTT) *DSIN 

THM{2,3) = -HLJ(JSTT) *ECOS 

THH{3,4) = 1.0 
GO TO 2000 
CONTINUE 
VE2TICL MEMBER KITH JOINT ON TH 



I- 3 



2000 



SET 

:nd 



trm 

TRM 

TRM 
GO TO 20 
CONTINUE 
VERTICAL 

TBfi. 

X-SB 12,4 

TRM (3,3 
CONTINUE 
URN 



-VUJ(JSIT) *ECOS 
-VOJ(JSTT) *DSIN 



THE RIGHT 
(DZZ (JTN) ) 
(DZZ(JTN)) 



E BOTTOM 
(DVV(JTN) ) 
(DVV (JTN)) 



MEMBER BITH JOINT ON T 
1,4) = VLJ (JSTT) *DCOS( 

= VLJ JSTI)*DSIN( 

= 1.0 



BE TOP 
DVV (JTN) ) 
DVV (JTN) ) 



11548*76 

11549*75 

11550*75 

11551*75 

11552*75 

11553*75 

11554*75 

11555*75 

11556*75 

11557*75 

11558*76 

11559*75 

11560*76 

11561*76 

11562*76 

11563*76 

1156 4*76 

11565*76 

11566*76 

11567*76 

11568*76 

11569*76 

11570*76 

11571*76 

11572*76 

11573*76 

11574*76 

11575*76 

11576*76 

11577*76 

11578*76 

11579*76 

11580*76 

11581*76 

11582*76 

11583*76 

11584*76 

11585*75 

11586*75 



" iH?£2H!H T -P JS * S S DETERMINES THE SHEAR MOMENT CCUPIE AND ONE 
- STIFFNESS ELEMENT WHICH IS REQUIRED TO FOEE STIFFNESS MATRIX 



************* ******* ****** ******** SUBfiOOTINF 
' SUB8OU^INE m DJSTSH^J[JTN f STF0,S_HM0jt 

COMMENT 

COflKEST - FOR EACH JOINT. IT CALLS SUBROUTINE 
COMMENT - THE DEFORMATION HISTORY. 
IMPLICIT EEAL*8 (A-H, O-Z) 
DIMENSION GABCOM(03),TAUCCfl(03) 

i(25f. *(25), 
SXX(25), SYY(2$ 
DZZ(25[, 
EBYY{25J, 



JNTBAS TC KEEP TRACK OF 



:(25) , 



COMMON /BLOCK1/ 

2 QZz'*~ 

3 DYYi 

4 ERXX(25j, 

5 USXX(25) , 

6 HSYP (25) , 
COMMON /BALAO 



HXXJ25J 

EEZZ(25 
NSZZ(25 



I: 



QXX 
SZZ 
RYY 
QMJ 
IMJ 



251 , 
25) , 

25), 

25;.; 

25 , 




V 



2W (25) 
NSVV^25J 



2 BVV(25) 

COMMON /3AL 
2 THKJ(25),GJ{25),SJC"(25) 

" / NIT/ APE03 



SW(25) 



DVV (25) 



NSXP"(25/, 
ERVV(25) , 



f°U JST(25),NJSS(25),HLJ(25),HRJ(25),VLJ(25),VUJ(25) 



08) , JSSf 08) , NTAU(0 
I8[.TAUHLT(08) ,GAMBLTf08) 
UEL(08,03), TAOfiAX(08,03 



1000 



1100 



1200 



COMMON 

COMMON /CHAi/13/ NPTJ( 08) 
2 NTAT(08) , NGAT(08' 

CCSaON /CHA12/ GAB- 

DATA PRINT /4HRINT/ 
100 FORMAT (/,5X,6HJOINT=, 13, 5X.13HSH. STIFFNESS 
210HSH.MOMENT=,1PE13.5,/) 
JSTT = JSI(JTN) 
IF (NJSS(JSTT> .EQ. 0) GO TO 1100 
NC = NJSS(JSTT) 
NPTH1 = NPTJ (NC) - 1 
DO 1000 K = 1.NPTH1 

TAUCOM(K) = TAUMAX(NC,K) *TAUMLT(NC) 
GAMCOM(K) = GAKIEL (NC,K 
CONTINUE l 

SLPHAi 
CALL JNTSAS 
GO TO 1200 
CONTINUE 

STFHIS 
TAUHIS 
CONTINUE 

STFJ = STFUIS*SJC(JSTT) 
SHBOJ = TAUHIS*SJC(JSTT) 
IF (APRCB .HE. PRINT) GC TO 1300 
PkINT 100, JTN, S1FJ,SHMCJ 
1300 CONTINUE 

RETURN 
END 



)*GABKLT(NC) 

= TAUMLT(NC)*NTAU(NC,2)/GAflHLT(NC)/NGAM(NC,2) 
(TAUHIS, 3tFHIS,TAUCOM,GABCOM,N£TM1, JTN, SLPMAX) 



= GJJJSTT) 

= STFHIS* (DZZ (JTN) 



DVV(JTN) ) 



************************* ******** 

1 1587*80 
11588*80 
11589*80 
11590*80 
11591*80 
11592*80 
11593*80 
11594*80 
11595*80 
11596*80 
11597*80 
11598*80 
11599*80 
11600*80 
11601*80 
11602*80 
11603*80 
11604*80 
11605*80 
11606*80 
1 1607*80 
11608*80 
11609*80 
11610*80 
1161 1*80 
11612*80 
11613*80 
11614*80 
11615*80 
11616*80 
11617*80 
11618*80 
11619*80 
11620*80 
11621*80 
11622*80 
11623*80 
11624*80 
11625*80 
1 1626*80 
1 1627*80 
1 1628*80 
11629*80 
1 1630*80 
11631*75 
1 1632*75 



08,08) ,NGAB(08,08) 

) 
1PE13.5,5X, 



342 



********************************** SUBROUTINE ********************************* 

SUBROUTINE SUIT (AA.BB.CC, IE! ,ID2,ID3) 11fiqT*75 

COMMENT - SUBROUTINE MULT HILL MULTIPLY A 1*1X102 MATRIX AA TI"!ES A 116^*7? 

pension ^4^4,4}, cc(4,4> jlgg 

D0 1 °cc/T If 1 ? 3 /, n 11639*75 

do ^oVl'V.Il2 ' JttfSB 

CC(I,jf = CC(I,J) + AA(I,K) * BB(K,J) 11642*75 



10 



JLMU 11644*75 



IMPLICIT REAL*8 (A-B,0-Z) 11648*75 

DIMENSION AA^ ^ B8(4.»J *7 ? 

RETURN J U ' J ' USHItt 



2ND 



11653*75 
11654*75 



?£*£«£?*.£*£*.*. *************** SUBROUTINE ********************************* 

SUBROUTINE TGCUE { NC . IABAN ) 11655*79 

COMMENT - SUBROUTINE TGCUE DEALS BITH THE DECOMPOSITION OF THE 11656*7? 

£RSSSS! * ? A J IC B . ISPDT INT i G EB CURVE NUMBER NC °* vi > ±llul > 0f Ta£ 1ll|f*79 

SRSSISS " J FOfi TdE SPECIAL CASE OF MILD STEEL, ONLY ONE COMPONENT IS 1658+90 

ggggfSS : L s S H D ADA T T?c £T 8 f I^i^L^IS 8 * 3 0F vlaGIH STBA1N hahdesiIg : 

illlll : |||S|!xf||tfof A sii€is^^ %m,m& UtVjnmLsmt" : 

LUHMEhT - HASiNG MODEL ( ALPHJ = . BETJ = \ 11fifil*7Q 

COMMENT - BASING KITH DEGRADATION ALPHJ « '. BETJ = 11664*79 

COMMENT - SPECIAL FCS MILD STEEL | ALPHJ * ' BETJ t 11665*79 

COMMENT - FOR THE PEESENI, INELASTIC CASE IS RESTRICTED TO SYMMETSIC 11666*79 
CURVES WITH THE NUMBER OF INPUT POINTS LESS THAN OR EQUAL TO 1667*79 

M ■ MSSINL ) INCLUDING ORIGIN (0,0) U 11668+79 

- DESCENDING BRANCHES ARE NOT CONSIDERED AND HENCE MUST NOT 11669*79 

C BE INPUT 1 1*70*70 

COMMENT - NO LIBIT IS PUT ON MAXIMUM STRAIN 11671*79 

IMPLICIT REAL * 8 (A-H , C-Z) 1 167?*79 

DIMENSION 0.0,(08), «W(08[, EHAX(07) 11673*79 

%s m*, wis 'sit! 31 >n]ii]% > 6SSI h D18 , . : 

90 FORMAT finr «om«i«« /^d .,««•-»■« „„».„„„ „„_..., . 



C 
COMMLUT 



2 



10X,37UDETAILS CF EASIC STUES S-STSAIN CURVES,/, 1 0X, 
z 24HSCALING FACTORS EXCLUCED,/) iiSfi?*79 

'10X,14HCUEVE NUEBEB = ,1 4, 5X ,25H V OF COMPONENT S»BI'" 



11661*79 
1 1682*79 
11683*79 



100 2 F I4) MAT < 10 *' 1 " HCnEVE NUEBER = ,1 4, 5X ,25H # OF COMPONENT SPRINGS - 

1 °V^i A lY n sTP&J a n P S ^ AIKS ' 6X ' 9H STRESSES, 6X,12HSTIFFNESS OF,3X, 11685*79 

£ UHflAX bijiiSS OF,/, 11686*79 

& l^'^^NPUT^iqx^HINPUT.IOX.IOHCOMPOHENTS.SX.IOHCOMPONENTS,/, 11687*79 

I 1 ° X ' ?XiJfi5ll??K i'*f#""tI««8HSJ ,5X,10H(UNSCALED),6i. " 11688*79 

.~, D lua (uHSCALED) ,/J 11689*79 

103 FORMAT (//,5X, 25HDEGRADATION YIELD GROWTH,/, 11690*79 
, ., 2 „„, m . 2 X ' , 5HALPHJ,8X,4HBETJ,//,5X, 2(Flo'4 ,3X),//) 11691*79 

104 FORMAT (//,5X f 43HDEGRADAT ION DEGRa5aTI0N flELD GROWTH YIELD, 1 692*79 

1 > 'S» G I9,f?H* 49H SMALJ SLOPE GAHHA SLOPE ULTIMATE. 1 1693*79 

11695*79 
11696*79 
11697*79 
11698*79 
11699*79 
11700*79 

■ ■■ ' ' 11702*79 

122 FORMAT 7//,36H ERROR IN INPUT OF TAU-GAHMA CURVE #,13,/, 1703*79 

2 39H DEGRADATION ALGORITHM (ALPHJ # 0) DEFINED ONLY IF CURVE IS. 11704*79 
,„ 3 20H CONTINUOUSLY CONVEX, /,20H (EXCEPT FOR "MILD")) •-"»»*• "« 1 705*79 
124 FORMAT J/A25B ♦*** BABfifM FOR CURVE l.xl.SH ****i/, 11706*79 

1 ill ?$SIg§ HOBELSITH CURVE NOT CONTINUOUSLY CONVEX IS PERMITTED, 1 1 707*79 
J I4H Al USEiiS RISK ) 11708*79 

12b FORMAT (//,36H Efil-lOS IN INPUT OF TAU-GAMMA CURVE #,13,/, 11709*79 

2 40H 4 POINTS MUST 2E USED FOR "MILD" CURVE ) ' ±J '/' 11710*79 
130 FORMAT (//,5X,28H ALPHJ MUST BE BETWEEN 8 \ ) 11711*79 
132 FORMAT //, 5X,J4H****SAHNING : ALPHJ SEEKS HIGH****,//) 11712*79 
134 FORMAT //,5X,18H iiETJ MUSI BE > ) '"' 1 713*79 
HS IS12 AT {/A5X,37H***HARNIliG : BETJ SEEMS VERY HIGH****,//) 11714*79 
13b FORMAT (// 5X,47HSLCPS FOLLOWING YIELD POINT MUST EE EITHER ZERO, 11715*79 

2 H7H OR A NOMINALLY SMALL POSITIVE VALUE FOR "aiLD",//) 11716*79 

DATA MILD /4HMILD/ ' //j 1717*79 




343 



180 



190 



200 CONTINUE 
205 CONTINUE 



„„„ m NAGAIN = 
CONTINUE 

KPT = NPTJ(NC) 
DO 190 J = 1,NPT 

QQ (J) = NTAU 

WH (J) = NGAM 
CONTINUE 

NPTH2 = NPT - 

NPTM1 = NPT - 
( NPTH2 .EQ. ) 
200 J = 1,NETH2 

SL~~ 

SL 

S 

EMAX (J)=HW(J + 1) 



<ic.a, 



t*c; 



IF 
DO 



GO TO 205 



LOK=rQ0(J+1)-QQ(J))/(a E (J + 1)-HH(J) ) 



* STF 



300 



350 
370 



380 
390 



400 



1410 



COMHENI - 



420 



STF 

RaAX(NPTfi1)= 
IF ( aATEJ(NC) .£0 
IF ( BETJ NC) .If 
IABAS = 1 
FBI NT 120, NC 
SO TO 1000 
CONTINUE 

DO 350 J = 1,NPTH1 
IF J RMAX (J) -GE. 
GO TO 370 
CONTINUE 
50 TO 390 
CONTINUE 
IF ( ALPHJ (NC) 

IABAN = 1 
PRINT 122, NC 
GO TO 1000 
CONTINUE 
PRINT 124, NC 
CONTINUE 

SKLSLJ 

GASTHD 

SLPHDJ 

TAUULT 
GO TO 500 
CONTINUE 

IF ( NPT .EQ. 4 ) GC 
IF ( NAGAIN .EQ. 1 ) 

IABAN = ' 
FEIST 126. NC 

GC TO 1000 

CONTINUE 

NTEHEA = 1 

NIEHEB = 1 

ALPHJ (UC) 

LPHJ IS SO* 



. RUE ) GO TO 400 
. 1. OD-10) GO TO 30 



0-0 ) GO TO 350 



LT. 1. OD-10 ) GO TO 380 



0-0 

10000,0 * H«(2) 

0.0 
QQ(NPT) 



/(BS(NPT)-HH{NPTH1) ) 





TO 

GO 



410 
TO 



500 



IF 
IF 



ALPHJ (NC) 
2MEA = 



COHMENT 
CGSaENT 



NTE 
CONTINUE 
IF ( BETJ (NC) 
BETJ IS NOT 
ZEEO- HOIEVEE 
BETJ(NC) =0.0 



. GT. 1- OD-10 ) GO TO 
INPUT FOR MILD(STEEL) 
= 0.1 ' 



IF 
AS 



. <iT. 1- OD-10 ) 
INPUT FOR MILD 
IT IS CUTPUT UNDER 



GO TO 
XSTEEI) 



420 

, USE A REASONABLE VALUE 



440 

, THEN IT IS TAKEN 

HE 'COMPUTED' TITLE. 



440 



500 



( 

KW 



NTEKF3 = 
CONTINUE 

SMLSLJ 
GASTHD 
SLPHCJ 
TAUULT 
NPTJ 

NAGAIN ' ' = 1 
GO TO 180 
CONTINUE 
PRINT 9 
90 
100, NC, NPTM1 

sxr = RaAxrj 






(3)-QC(2) ) / ( 



) / ( 



= ^w ] 



»8(3)-IH(2) ) 
BK(4)-MH(3) ) 



800 



COMMENT 
C 



PRINT 
PRINT 
PRINT 
PRINT 
PRINT 
DO 

/ SW(J 

CONTEST'' ™ Wi ' STF ' EHAX 
DO 900 J = 1,NPTM1 
GAMIEL(NC,J)_ AHD_TAUHAX(NC, J) 



OF 



the 'basic 

G A KIEL 
TAU MAX 
900 CONTINUE* 

IF { MATRJ 
PRINT 103, ALPH 
GO TO 982 
950 CONTINUE 
PRINT 104 

IF ( NTE3PA + N 
IF ( NT EKE A - EQ 
IF ( NTEMPA , BE, 



. PERTAIN 
INTEGER INPUT CURVE NUMB 

NC,J) = WW(J+1) 
NC,J) = RMAX (J) 



TO THE JTH COMPONENT 
Efl NC 



(NC) . EQ- MILD ) 
JJ(NC), 3ETJ(NC) 



GO TO 950 



i»Pb .EQ. 
.AND. 

.AND 



-2J. 



GC TO 980 
1 GO TC 970 

PRINT lJ5"," ALPHJ VnC), BETJ (NC) ^ 3 Silt J ( NC) , GASTHD ( NC) ?IlPHDJ (NC) , 



NTEaPB 

NTEMP3 



. NE. 
EQ. 



11718*79 

11719*79 

11720*79 

11721*79 

11722*79 

11723*79 

11724*79 

11725+79 

11726*79 

11727*79 

11728*79 

11729*79 

11730*79 

11731*79 

11732*79 

11733*79 

11734*79 

11735*79 

11736*79 

11737*79 

11738*79 

11739*79 

11740*79 

11741*79 

11742*79 

11743*79 

11744*79 

11745*79 

11746*79 

11747*79 

11748*79 

11749*79 

11750*79 

11751*79 

11752*79 

11753*79 

11754*79 

11755*79 

11756*79 

11757*79 

11758*79 

11759*79 

11760*79 

11761*79 

11762*79 

11763*79 

11764*79 

11765*79 

11766*79 

11767*79 

11768*79 

11769*79 

11770*79 

11771*79 

1 1772*79 

11773*79 

11774*79 

11775*79 

11776*79 

11777*79 

11778*79 

1 1779*79 

1 1780*79 

11781*79 

11782*79 

11783*79 

11784*79 

11785*79 

11786*79 

11787*79 

1 1738*79 

11789*79 

1 1790*79 

11791*79 

11792*79 

11793*79 

11794*79 

11795*79 

11796*79 

1179 7*79 

11798*79 

11799*79 

1 1800*79 

11301*79 

1 1802*79 

1 1803*79 

11804*79 

11805*79 

11806*79 

11807*79 

1 1808*79 

11809*79 

1 1810*79 

1181 1*79 

11812*79 

11813*79 



344 



2 GO TO 932° 0I ' T(NC) 11814*79 
960 2 PEINT 106, ALPHJ^NC).BETJ(KC) F SHLSLJ(SC),GJSTHD(NC),SLPBDJ{NC), 11816*79 

GO TO 982 11817*79 
970 2 PRIBT 107, ALPH^NC),BETJ(NC),SHLSLJ(NC),GASTEB(NC).SLPHDJ(NC), 11819*79 

GO TO 982 11820*79 
980 2 PSOT 108, ALPHJ(KC),BETJ(NC),SBLSLJ(NC),GA5THD(NC),SLPSDJ(NC), 11822*79 

982 CONTINUE 11823*79 

IF ( tH?« ( ^ C) i ,GE - °'° - AND " ALPHJ(NC) .LE. 1.0 ) GO TO 984 11825*79 

PEINT 130 "' 11826*79 

GO TO 1000 iiooZt^ 

984 CONTINUE ll 8 , 2 , 8 ,* 7 ^ 
IF I BATBJ(NC) .NE. BILE ) GO TO 985 1lRin*7Q 

PfiINT F li2 ALPHjlNC ' ' LT * °-^) GO 10 985 11 111 J?! 

985 CONTINUE 11JN3J?! 
I? ( ?fft?,l HC) ,' G *- °*° > GC T0 986 11834*79 

PEINT 134 " 11835*79 

GO TO 100(1 11836*79 

986 CONTINUE 11837*79 
IF I HATSJfNC) .NE. BUD ) GO TO 987 lljnt*?! 

PEIN| F lJ6 BETJ(ic) ' LE - °- 8 » G ° T0 987 BJJB 

987 CONTINUE 11841*79 
IF { SHLSLJpC) . GE. 0.0 ) GO TO 1000 11843*79 

PBINT 138 " 11844*79 

1000 ^CONTINUE HlSftfa 

£alJ 11848*79 
********************************** SUBBOUTINE ********************************* 

DIMENSION GAMCOH(03), TAUCOfl(03) 1iasi*«n 

,C0««O| /BLOCK1/ i(25f, Z<25), QXX (25) - nn,w JliiSIR 

2 QZZ{25), SIX (25), SIY(2$>. SZZ?25{ 

3 DYY|25j; DZzbsi; EXX Hij J Iyy}25J 



QYY(25j, 11854*80 
DXX{25), 11855*80 



BYY(2Sj, BZZ|25), 11856*80 

1 5llfjff$jl* Ili?f3§l' EBZ2 (25) , QBJf25), WHJJ25L. 11857*80 

1 lillill ; IlJJlliif NSZZ ^}, SritfiJ, nsxp(25;, iislajeo 

2 co "g^ii," 8 v mmi SVT(25) ' D¥Y(25) ' ee7vj25 >- fffrig 

COaSOH /3LK1/ TOL, ELEHNT, NJST, KEEP3CNCD3C, 11862*83 

2 ££,?,£?«, KEEP3A,KESP3B,KEEP4A,KEEP4B f KEEE46,KEEP5 A, 11863*83 

3 KEEP5fe,KEEP5C,KEEP5D r KEEP6,'KEEP7,'NCD2, NCD3A, 11864*83 
I NCD3B, NCD4A. NCD4B, NCD4C, NCD5aJ NCD5B, NCD5C' 1 865*83 

1 S?£?5» 2S D6 ' NCD7 ' IP8 » Ip9 » IP10, ITYPE, 11866*83 

6 IA3AN, IFOBK, NS, NJI, NST, NIT, H, 11857*83 

7 ^ 1 * «E2, I Sit. LTT' ITY^EL,IDj; NSTL 11868*83 
COBHON /BLK5/ NFSU6,NITF,N^,N2 ' 869*80 
CCflMON /SKT3/ NCOUNT, NITEEF 11870*80 
COBHON /SKT6/ NITEBHJ50) , INDEX 11871*80 
CCHHON /SKT14 / IBVJ2 1,2,f 0) i ' FOHCLD (SO, 6) , 11872*80 

2 IEVESE, ITAPE, N3 11873*80 
CCHHON /SKT18/ NCHECK 11874*80 
COHHON /5KT22/ TIHE, JT, IHDYN, IESTEP(71) 11875*80 
COHHON /CHA13/ GAHES (2S;3) , GAHRTS (2 5, 3) 11876*80 

„ COHHON /CHA19/ JR V (25) ,3sGICN (25) 1 877*80 

25 9 F i§S A Ii4b^ H * rS0 Tlnn' 50INT ^* ;i: 4/fi 12H STEAIN =,1PE10.3,/, 11878*80 

2 12H TAUHI5 =, 1PE1 0.3. /, 12H STFHIS =,1PE10.3f 11879*80 

§Ig&i = CZZ(JTN( - DYV(JTN) ' 11880*80 

TAUHIS » 0.5 11881*80 

STFHIS -0.0 118fl?*R0 

j f o ijst=i;«^ go io 4i ° ill; 

400 CONTIN G uT S(jfN ' K) = «"«(«..«! 11BB5* 

410 CONTINUE 11887*80 

DO 1200 K = 1,NFTfl1 11888*80 

SLOPE = TAUCOH(K) / GABCOH(K) 11889*80 

H„ : GAMES fjiw,K( 11890*80 

EET = GABBTS ( JTN,K) 1189 1*80 

IF ( DABS (STRAIN-EB) - GE. (GABCOH (K) -5. OB- 1 0) ) GO TO 500 11892*80 

C LINEAB ZONE ( BEGIN ) 11893*80 

STFHIS = STFHIS + SLOPE ' 11894*80 

SO = SLOPE *(STEAIN-EB) 11895*80 

IF ( NCHECK -NE. 1 ) GC TO 450 11896*80 

C0BH2NT - ONLY FIRST COBPONENT NEED TO BE BONITOBED FOE SEVEESAL. 11897*80 

IF ( K .HE- 1 ) GO TO 450 11898*80 

IF ( JRGICN(JTN) .EQ. ) GC TO 450 11899*80 

m Tn J ??n^ J N) = 1 11900*80 

450 g o^inu! 0(3 i 1 -JI3j:i8 

£0H3ENT - DURING ITERATION PEOCESS IT IS POSSIBLE THAT THE STEAIN 11903*80 

COHMEKT - RIDES INTO PLASTIC RANGE, AND THEN COHES INTO THE ELASTIC 11904*80 



345 



COMMENT 
COMMENT 
COMMENT 
COMMENT 



EST = EE 

INDEX ,£Q, 1 ) GO TO 1000 

K . NE. 1 ) GO TC 1000 



LINEAB ZCNE 



IF 

IF 



JBGICN(JIN) = 



GO TO 1000 
500 CONTINUE 

IP ( STB A IN .GI. 



( END ) 



EH 



.. )GC TO 600 

NEGATIVE HELD ZONE ( BEGIN ) 



IF 
IF 
IF 



SO = -TAUCOH(K) 
NCHECK .BE. 1 ) GC TO 



550 



K .82. 

JRGICN (JTN) 

JRV (JTN) = 
GO TO 2200 
CONTINUE 

ERT = 

INDEX 

K 



n 

. NE. 
1 



GO TO 550 
1 ) GO TO 



550 



IF 

IF 



C 

c 



GO 



600 

650 

Z 
1000 

1200 CC 

2050 
2100 



STBAIN + GAMCOK(K) 
•EQ. 1 ) GO TO 1000 
-HE. 1 ) GO TO 1000 
JRGICN (JTN) = -1 
T0 10 - Q0 NEGATIVE YIELD ZCNE ( END ) 

SO = TAUCC^(If IVE " E " ZOl,E ( BEGIN » 
GO TO 650 
GO TO 650 
- -1) GC TO 650 



IF 
IF 

IF 



NCHECK -NE. i 
K .NE. 1 

JRGICN (JTK) .11 
JRV (JTN) = 1 

GO TO 2200 

CONTINUE 

EST = STRAIN - 

IF ( INDEX .EQ. 1 ) 

IF f K . NE. 1 ) 



GAflCOM(K) 
GO TO 1000 
GO TO 1000 



HTINIJE 
IF 
IF 
GO _ 
CONTINUE 
IF (HITF 



JRGICN (JTN)_ = +1 

POSITIVE YIELD ZCNE 
IA0HIS - TAUHIS + SO 
GAMES (JTN,K) = Efi 
GA2RIS(JTN,K) = EB1 



( END ) 



.LE. 2 
.EC- 1 



) GO 
.AND. 



TO 2050 

BITES* 



.EQ. 2) GO TO 2100 



.EQ. 2 -AND. NITEBF . EQ. 2 ) GC TO 2100 



2200 
COMMENT 
COMMENT 



2500 



SB 



EN 



GO TO 2200 

CONTINUE 

IF ( JEV(JTN) .EQ. ) GO TO 2200 

STFHIS = SIPMAX 

JBV(JTN) = 

lT| E § A f!R^N S !I 5 A VE STEAIH EXCEEDS THE LAST STBAIN 

DA M H f^ I Q! ,) rf T Gc G T A o BC ^§ PTfll) > S0TC2500 

, JTN, STRAIN, TAUKIS, STFHIS 

INUE 

NCHECK .EQ. 1) IRVBSE = IBVfiSE + JR? (JTN) 



CONT 

- OUT? 

- ORDI 
IF ( 
IF 1 

INT 25 
CONT 
IF ( 

TURN 

D 



11905*80 

11906*80 

11907*80 

11908*80 

11909*80 

11910*80 

1191 1*80 

11912*80 

11913*80 

11911*80 

11915*80 

11916*80 

11917*80 

11918*80 

11919*80 

11920*80 

11921*80 

11922*80 

11923*80 

11924*80 

11925*80 

1 1926*80 

11927*80 

11928*80 

11929*80 

11930*80 

11931*80 

11932*80 

11933*80 

11934*80 

11935*80 

11936*80 

11937*80 

11938*80 

11939*80 

11940*80 

11941*80 

1 1942*80 

11943*80 

1 1944*80 

11945*80 

1 1946 + 80 

1 1947*80 

11948*80 

11949*80 

11950*80 

11951*80 

11952*80 

11953*80 
11954*80 
11955*80 
11956*80 
11957*80 
11958*80 
11959*80 
1 1960*80 
1 1961*80 
11962*80 
11963*80 
11964*80 
1 1965*80 
11966*80 
11967*80 



****************** ** ************ 

SUBROUTINE DYNAJS (HM, BO, 
CORMENI - SUBROUTINE DYNAJS PEIiFO 
COflSENT - INCLUDE JCINT SHEAS DEF 

IMPLICIT EEAL*8 (A-E,0-Z) 

REAL*8 MEMBER 

BEAL*4 DISJT 

EEAL*4 FOBCEL, STEASL, BHOH 

2 FORCER, STHANB, BMOM 

3 FKHAXF, FRKAXD, FBMM 

4 TOAXF, TOAXD, TOMO 

5 SHMJT 
FOMTEM 

SMHT 



** SUBROUTINE ********************* 
S, SL. 11, L3, L4, L6. DELWJT ) 
BBS DYNAMIC ANALYSIS FOB FRAMES TEAT 
CEHATICN EFFECTS. 



NL, CUBVAL, 

Nfl, CURVAR, 

CM, FEMROT, 

M, 1CR01, 



REAL*4 _ 
DIMENSION 
DIMENSION 
DIMENSION 
DIMENSION 
DIMENSION 
DIMENSION .. 
COMMON /BLOCK 1/ 

2 QZZJ25- 

3 DYY (25 

4 ERXX(2_ 

5 NSXX/25 
b NSYP (25, . 

ccaaoN /BALAU1/ 
2 SVV (25) , 

COMMON /BL0CK2/ 
2 DC2S ( 25) , 



Ik 



21) 

6} 

__M(50,6 

7]) 

Lo,L4) . 

KJT (16 
X(25 
SXX (_ 
DZZ (2 
ERYY( 
NSYYf 
ISTJR 
QVV (2 
NSVV( 
DXS ( 
PKF ( 



L61 



BO(L6) , W(L6) 



2 if* 

(25f 



25 
25 



SYY (25) , 
SXXi25[ . 
ERZZ(25), 
NSZZ(25) , 

SVV (25) , 

DYSJ 25), 
PRAE( 25) , 



SHFOBL, GAKMAL, 
SHFORS, GAMMAB, 
FBMSHF,FRMLTD, 
TOSHF, TOLTD, 



BIU33 




DVV(25) , 

ZLS( 25) , 
QH< 25), 



QIT{25) , 
DXX(25) , 
SZZ (25), 
WMJJ25[, 
NSXi{25J. 

ERVV(25) , 

DC1S( 25) , 
BH( 25), 



************ 
11968*82 
1 1969*90 
11970*90 
11971*82 
11972*82 
1 1973*82 
11974*82 
11975*82 
11976*88 
11977*88 
1 1978*88 
11979*82 
11980*82 
11981*82 
11982*82 
11983*85 
1 1984*82 
11985*82 
1 1986*82 
11987*82 
11988*82 
1 1989*82 
11990*82 
11991*82 
11992*82 
1 1993*82 
11994*82 
11995*82 



346 



COM. 



PBAG125). ELEBN{25), 1iqqs*fl9 

J??9m=: 25 >' S PI J ,L < 2 M, IPIHH( 25), KC51( 25), INLOP( 25). 1 1997*82 

\mMl hsisi; mum imffi t st&Jj** *1 

COHBOB /|LptKV FO|M50;6),SHCf50,21) ,IST{50) . LT(50), 12002*82 

1 bIIs^), g|i,fi J. Hi Hi li |1 ' -^'/22). 
2 C0« M 0K^B,0CV W „ 25] » fi f5gp|"l ) f F»« 3 [25^ !i M i Z,2 a * 

C0Ha 0N /8L0C1§/ Z&Xiij'l 5,25) JsYXBJ (5,25), EBZZHJj$,2$f, ( ' 20 2*82 

2 DXXJiJfS-25) #BIXHaf5.55l,D2Zaj(5;251,K0HJ(5.25) JiCOJf"" 

COHfiOH /b£lA16> EBVVMJ/§.25f .DVVN.I^T?*;? * ' '' l 



CCflaOH /BL0C21/ ACCJT (TOO) ,V3LJT(10of ,ZHASSP(100) .DACCJTdOO) 12015*85 

2 co HB giTB^c25^iiip;55T ZT}25i - DFjWi2 ^ II: I 

C0HBON/BL0C24/ AN 1 (40 [ , AN2 (1 1) ,NPBOB (2) 12020*82 

COBMON /BLK1/ 101,' ELEBN1, NilST, KEEP3C, NCD3C, 12021*82 

1 SSISi* KE!£3A,K£EP3fi,KEEP$A,KEEP4B;KEEP4C,KE£P5A, 12022*82 

3 KEEP52,KEEP5C,KEEP5D,KEEP6, KEEP7, NCD2, NCD3A, 12023*82 
| «CD3B, NCDUA, NCD4B, NCD4C, NCD5A^ NCD5B, NCD5C, 12024*82 

5 NCD5D, NCD6, NCD7, IP8, IP9, IP10, ITYPeJ 2025*82 

6 IABAN, IFCEB, Nfi, NJi; HSt! NLT, B, 12026*82 

7 „„„„„,, MP1. HP2, ISTT, LTT, ITl*BL,XDj! NSTL 12027*82 

^ KNPLS.ailiSS, MNQWH, HRJST, HNJSS 1?0?q*R? 

ccaaos /blks/ nfsob,nitf,ni,h2 12030*82 

S855ni < B ^ 7 < J? l °p|» I^AE, k6ffj,K0FFQH,KOFFSE 12031*82 

coaaoh / hi / nl, kl, ji i:>m?*R? 

COflfiOH/ITC/ EBfi1.E3B2,EBl,EB2,DII,CB,NTI.BH(20),flJ(20),BNITF, 12033*88 

^ fli»ITK, NSflJ,NSBM 12014*88 

COMMON /WABN/ NJNC,NMNC 12015*8? 

CCaMON /NIT/' A? BO 3 12036*82 

COBHON /SKT2/ WEX(25,10), *BX(25.10), KBZ(25,10), 2037*84 

2 . KBV 25,10), ISXP(2S,lbj, WF.YP(25,10), H8TX(2§.10)' 12038*84 

4 SiSfJ^Hf "anUSJioi: hbt?1&:io ', wiil^.M, 12039*84 

4 WEXIP (23, 10) 1?040*Rtt 
COaaON /SXI3/ NCOONT, NITEBF 12041*82 
COSKOH /3KI5/ jiBXfl (21,10), WBYB (21,10), HEZH (21,10), 12042*82 

2 KfiTXfl{21.10j . BHTYH(21,10J I tfBTZfl (2 l' 10j 12043*82 

CCaaotl /SKT6/ NITEBB(50). INDEX l?nuii*«9 

COHBON /SKTl'l/ BSSINi; '' MSSIB1 l5045*8? 

COMMON /SKI 13/ EPK1S(21,10,3),EPBI1S(21,10,3), 2046*82 

2 cOKMnH /-^-n-ui / TD 2P22shl.10,3J,EPBT2S 2i;io;3 ' 12047*82 

COBMON /SKT14 / IBV (21,2,10), FOB01D (50, 6) , 12048*82 

2 coa«o N /SKT15/ $r sE - itm?e - n3 ijifgrsj 

COMMON /5KT17/ N4 12051*8? 

COMMON /SKT18/ NCBECK 12052*82 

CCaaON /SKT19/ JCBGON (25,6) , JCnEEV(25,6) 12053*84 

COMMON /3KT2 0/ HCBGONJ2i;3 K HCOEEvbl'3 12054*82 

COKBON /5KT21/ NTH, NtfBA l * ' 12055*82 

COMMON /SKT22/ TIME, JT, IBEYN, I3STEE(71) 2056*82 

CCSBON /SKT26/ LTYPEL V ' 120*7*82 

COBMON /SKT27/ IBEAD, IHBITE 12058*8? 

COMMON /SKT28/ FOECEL ( 20, 71 ) . STRANG (2 0, 71 ) . BBOHH1 ( 20 , 71) , 12059*88 

2 CURVAL(20,71),FOBCEB(20 / ,tl) , STBANB? 20 ,7 1) , BMOBNB'{20 ,7 1) , 2060*88 

3 CUBVAfi(20,71) ,FRaAXF(20,71 , FHBAXD (20 ,1 1) , FEBBOB (20l71 ' 12061*88 

4 FEaaOT?20,71) ,FBBSHFl20l71 ^F3flLTDJ20 17 1 | XOAXF (20, 7 1) , ' 12062*88 

5 TOAXDfio,^ 11, TOaCB(i0,71) J ,'lOROT(i0,71);'TOSHF 20',71 12063*88 

TOLTD(20,71) 12064*88 
CC.1HON /SKT30/ aSTIF{25), BIOAD(25), H0DE1(25) 12065*82 
COBBOH /SKI32y EPEF1 (21,10,3) ,SPBFT1(21, 10, 3), SLBF1 (21,10,3), 12066*82 

1 SLBFT1 21,10,3 , EPBF2 jJlJloISj; EPBFT2 \2^W,% ', 12067*82 
J SLBF2 21,10,3 , 3LBFT2 (21 , 1 . 3) , " 12068*82 
I IZZ^Ui'l'hl' 2PSMI»}21,2,10J, EPSPHE(21,2,10), 12069*82 
5 ^ , !(GBOH 21-2, 10j, YTGBOW(21,2,10i 12070*82 

rrwr 'ASIW, UUZV 25 ' ' EBlfDN(25), EEZz6n(25), EBlTVDN(25) 12071*82 

Coaaoi /SKT35/ TBESTP 1?07?*fl? 

COBMON /3T/ fiio 12073+82 

CCBBON /CKA13/ GAMES (25,3) , GABBTS (25, 3) 12074*82 

CCBHON /CHA19/ JB7 (25) ,5s6iciJ (25) 12075*82 

7 C ° M2 ^ ; M^r^ / 7n HF ^i^5Z 1 ^? AHHAL(20 ' 71 >' SflFOEE ( 20 ' 71 )' 12076*88 

1 GAHBA2(20,7 1) ,£>HBJT (20, 71) 12077*88 

coaaoN /cHAii2/ sfeac(25) i?078*a? 

V&\ UiU^tEMU'^^ AHP^O/, SAVE /4HSAVE/ 12079*88 

DMA aaaaEB /4dBBEB/ i?oao*r? 

DATA AN0W/4HAN0B/,ANEI/4HANEH/ 12081*82 

AA1A SHEAB /5HSHEiB/ 12082*82 

2 !c1«il f^ofg 1 ! ,8 ° X ' 10HI TEI " > 12083*82 

l^i FUBHAT ( 20A4 ) 12084*8? 

1° S<??aAT (///, 1 7HPEOB(CCNTD),/,5X,A4,A1,10X,A5.7A8,A4,///) 12085*82 

18 jruBHAT {///,4X, 30HEESOLTS AT EKD OF TIKE STEP = ,15, §H AND ,12086*82 

, s 2 8H TIBE = ,F10.5,///) ' 12087*82 

20 F0BHAT(41HDXNAHIC SCLOTION FAILED TC CCNVEBGE AFTEE, 12088*82 

2 10H ITERATION, 13) ' 12089*82 
al Pnp«t? K<^ 2SX ' 1&HTI!1E STEP .I3,5X,7HTIHE = ,F10.4,//) 12090*82 
4T fOBBAT (1111) 12091*82 



347 



50 ? FOBHAT ( y| ppoBfOLDTIC^ABASDONED IN SEARCH C? AN INDEPENDENT 12992*82 

1 ' /y? ' ' IHE FOi^CIING CAHDS HEBE DISCARDED IN SEARCH, 12094*82 

90 FORMAT I ////) \ill\*A% 

9^FOSHAI \///.\ll D ™™g c T fg"«°VfI"5 " TIBE STEP = ,15, 12097*82 

94 FORMAT 1///.IM DYNAMIC SOIUTioN Fltttt'lBIIE TRYING TO PROCEED, 12099*82 

ill nwm&FAfflffiffi™ LAST G00D s °^«;.//> I !fc I 

98 FORMAT ( // ) "-""->/// I l^TUJ'b^ 

10 9 9 fglgii / ^1p2I^I 1 V ) ' / ' W* 1 ""^*./. M1PE11.3, ) |]8j;g 

|| I8I« A ? 3 3 ] H H SSih ?i23igU IU a a I 18! : '.Wl-l-'/A j gf:!I 

130 FORMAT 31H JOINT ACCLERATIONS AT TIME = .llolu'Vy lliol*!? 

SyOBIAf I//.48H £fiD o * IglCltgg ,«„ SOPFOtt'SJ^'iuHYB AT, 

155 ««*. C///30B ««, FRAME ITERATION NO 15 6H ,«•".//. * 

| U, 25H HEHBER EQULIBBIUH ERRORS,/, "«*""■" ' 12114*82 

S II* \%l 1 ??,r ITER r>* AIIAL LA^fiAL BOTATIONAL , 12115*82 

5 3X„ 32h AXIAL LATERAL RCTATIONAL1 l?li£*a? 

95 FOP^T }// 121 **$n BHME S *ll!if?°£ ,I°.i!P I" J0IBI SOLUTION **, If til 

125 ££Ss A I VJ^^Ck' 3J *H REVERSAL HAS BEEN SENSED ) 12118*82 

200_FORMAT |1H1,20(/),40H THIS IS AOTO TIME STEP REDUCT. PROBLEM 12119*82 



3 FORMAT (1H1,20(/),40H THIS IS AOTO TIME STEP REDUCT- PROBLEM 12119*82 

205 FORMAT ( 1H1 ,/, 1 X, 14HMEMBEB NUMBER , 13 , 2X, 1 9HMEMBEH RESPONSES IN 1?1?1*flB 
„„ 2 56H THE DIRE£ti6n OF ORIGINAL GEOMETRY- RECORDED FYSTERSIS //\' 121??*flfl 

206 FORMAT (lX,16|fl$BBE| IDHBBB = ,I3,26H--MEMBEB RESPONSE AT tW? 12123*88 

207 FORMAT ( 1X, 1 6 HHEMBEfi NUMBER = ,13, 26H— MEMBER RESPONSE AT THE , 12125*88 

210 FORMAT (20X,25H AT THE LEFT END — ,/) 12127*Rfl 

211 FORMAT 20X,2SH AT THE RIGHT END '/A 12128*88 

212 FORMAT ( U, 4HTIM£,/,37H STEP TIME AX. FORCE AX.DISPL , 2 29*88 

220 FORMAT MHlgJlX. SOMBER i§ilII°»X3 .ft f iiflcT^S- SIlfSftA IN, 1i^J?*tI 

2 56H THE DIRECTION CF DEFORMED GEOMETRY - RECORDED HYSTEFSIS /A 17l1:>*sft 

^FORMAT CMgI.jJ^.Dg.^.^3 |5Jj g MO.« OF*?!? Il^gf 1 ?'"' * 

^FORMAT 'Jftag&WgBn- ,13, 25H-RESPONSE OF THE SECTION . j|||;|j 

230 FORMAT (1X, 4ETIME,/,37K STEP TIME ' AX.FORCE AX. STRAIN, 12137*68 

,,,•2 22H MOMENT CUBVATORE,/) AA.o4.aAxn, 1^10/ do 

234 FORMAT (5X.44HTABLE 8 - JOINT DISPLACEMENTS. REACTIONS AND. 12139*89 

2 29 g SHEAR PANEL INTERNAL MOMENTS.///, 121 

3 57B JhT DISP7X) DISpm ROT (Z) RO. 121 

4 50ET(V) REACf(X) REACT (Y1 ,J RE ACTf 21 B^ACT m . ' o 



40*S 
41*? 



23b FORMAT (jx,1H*,I3,4'(1pil5.7),6'(1PEii:3j/ ' ' 
237 2 FORMAT^{65|.4|1lH -------ij ,>/, 60X, 5HT0TAL, 4 < 1 PE1 1. 3) , 

233 FCRHAT' (5X.34HTABLE 10 - JOINT EQULIBfilUB ERRORS, ///, 

2 4X -5HJ0INT. 3X. 6HSRR i f\ .f¥ _ f,BEC b7y\ inv ftnwop /9i *bV' tavnt 



1 PUH^Hr* Kr^PiJl koSt^PW 'bEACT(Z) "BEACT(T), 12142*89 

3 24H SHii.nCM(2) SHE . BOM (V),//) 12143*fl9 

235 FORMAT < 12. 14, 4(1Pfi15.7)i 6MPE11.3) ) 12144*83 

$ I2I5 A S iht*foltt'*b*ZK' 7 )' 6 V**V'hl 12145*83 

12146*89 

12147*83 

///, 12148*83 

OflENl,//) HEEB(V),/ ' 12150*83 

230 FORMAT (//,51H ** PRINT OPTION IS LIMITED TO # OF HEBBEBS + # OF ,12151*88 

2 16H TIME STEPS = 30,//) 12152*88 

251 FORMAT <20X,47H SECTION CLOSEST TO THE -FROM- JOINT./) 12153*88 

252 FORMAT (202, 47H SECTION CLOSEST TO THE -TO- JOINT / 254*88 

"3 FORMAT \1X, 4HTIHE,/,37H STEP TIME AX.FORCE AX. STRAIN, 12155*88 

-_,,*. „ ,. 44H MOMENT CU2VAT0RE SE. FORCE SH. STRAIN,/) 12156*88 

254 FCriKAT 1X,I3,7nPEl1.3)) " ' 12157*88 

255 FORMAT (2l3 ,F6. 3, 6 ( 1PE 10. 3) ) 12158*88 
25b FORMAT (1X,15HJOIUT NOKBER = , I3,29H--EECOEDED DISPLACEMENTS AND ,12159*88 

2 17HSHEAR MOMENT (Z) — ) 12160*88 

257 FORMAT (213 , F6. 3,5 (1PE12. 5) ) 12161*88 

2d0 FORMAT } 15H CHECK THE DATA) 12162*88 

777 FORMAT ( 48H *** SOLOTlON DID NOT CLOSE - STUDY MONITOR, 12163*82 

2 10fl DATA *** ) 12164*82 

NTSME = NTI * NM 12165*82 

IF ( APROE .NE. PRINT ) 30 TO 4C0 12166*82 

IF ( NTEMP .LE. 30 ) GO TO 400 12167*82 

.„„ ot , A PEIiI2 = EBNTNO 12168*82 

PilNT 250 12169*82 

400 CONTINUE 12170*82 

TEMP = NTI 12171*82 

TOTTME = TEMP + DTI 12172*82 

NTR = 2 73*82 

NJTT = 3*NJT 12174*82 

DO 410 I = 1,NJT 12175*82 

IF (JST(I) .EQ. 0) GO TC 410 12176*82 

NJTT = NJTT + 1 12177*82 

410 CONTINUE 12178*82 

J = 12179*82 

DO 500 I = 1,NJT 12180*82 

IF(ZBASS{I) ,GE. 0.0) GC TO 420 12181*82 

J = J + 1 T>182*82 

ZMASSR(J) = -ZHASS(I) 12183*82 

J = J + I 12184*82 

ZMASSR(J) = 0.0 12185*82 

GC TO 430 12136*82 

420 J = J + 1 12187*82 



348 



^KASSfi^ = ZMASS(I) Um*§2 

430 i a £ S ! 3 i J l| = Z " SS (I) iiiioJif 

ZMASSR(J) =0.0 iiiq?I«i 

IP(JSI(Ij ,£o/. 0) GO TO 500 12193*82 

500 COKTX^f 32 ^ 1 = °-° JIJIIJII 

DO 550 I = 1.NJTT 191Q7*fl9 

CDAnP(lf=CS*ZHASSB{I) 1?iqsifl5 

550 COSTINa| (ZiIA ^ E{I)) ' GE - 1 - 0E + 15 > CDABP{I,=0.0 12199*87 

IF (ITIPE .BQ, 4 )GC TO 900 1?9ni*fl? 

DO 600 I = 1,NJTT 12201*82 

VELJTfTl = a 12202*82 

600 CONTINUE TBLJT < I > °-° \\ilhll 

900 CONTINOlP °* ° 1I382S8? 

g88S!Si : tisVll £LS fSS I SS^I I ^aS5oT TP1B * 9 Pfi0BLEM ' THES 7AiDES m& 

IF ( ITYPEL .EC. 9 ) GO TO 940 itoii*! 2 . 

£83818 : *&F5§i?MH5SS? A i s c 8SFKS2 101 0F TTPE 1 os T " E 2 PB0B ^« 11 3*1 

IF if IT IP El , LI. 2 ) GO TO 1000 ^H!K 

gssHs; : T i LhiiT s . A i fi iA°^ A ^ cc s ^ i fEA A s ioN of type 3 ofi " pb * pBoB " a 11:11 

940 C-UlNol - EQ ' ° > G ° T ° 100 ° If 1:1| 

BEHIND 13 lioii:!? 

HEAD (13) IBEAD ??^J2? 

IF < ISEAD .EQ. 11 ) IHBITE = 12 12221*8? 

IF j IBEAD .BQ. 12 ) IWBITE = 11 i4H]l%% 

COHMEN1 - EEAfi OFF UNIT 'IBEAD' i??11I1? 

flEHIND IREAD Miii.ZS 2 , 



HEAD j IBEAD ) j DXX(I). DYI(I), DZZ(I), DV?(I). 1=1. NJT ) 12225*8? 



COMMENT - CUBVES «*"«■** -INDICATORS FOB JOINT SHEAR STRESS-STRAIN 12227*82 

DO 941*1 = 1,HJT i? 2 ?^ 2 

jaV(I) = 1??in*fl5 

941 CONTINUE i 22 o?*2 2 

DO 942 I = 1.NJ1 3^1!S? 

if ( SISS : a gf x J<f>ss s i5tHj«a(i)«s T T(i)*isxP(i)«siP(i) iiiIjII 

READ (IBEAD) (HEX (I , J) , HBTX (I, J) , HEI (I, J) ,HBTI (l # J) , HEZ (I. J) , 12235*84 

COHBENT - INITIALISI BEVEfiSAL IBDICATCB3 FOE JOINT COBVES 12239*82 

E§ 121 i = ];! BJI 12240*82 

945 CONTIN0l fiEV(I ' N) =° \M& 
5225123! " IS.SII LAST G00D SOLUTION STCBED ON UNIT 'IBEAD* WAS ENDING IN12244*82 

CCHBENT - STATIC ANALYSIS THEN, VELOCITIES ETC. ABE NOT APPLICABLE 2245*82 

BEa/VibI SV ST) |iS|;^ vlLJT E (i) E ?-I= 3 llN^T T ) C 95 ° llj|fe|j 

950 &EAD C0 ]tI^ D > ^CCJTU), I=1.NJTT) jjg| ; g 

BEWIND N2 l??qo*fl? 

BEHIND N4 IsSllJsi 

DO 980 JJ = 1.NH 12252*82 

ISTT = ISTfJJ) 12253*82 

IF { ISTT . EQ. ) GO TO 980 12254*82 

MODELI = HCDEL(ISTI) 12255*82 

ELEKNI = ELEHNjlSTTJ 12256*82 

NHINGE = 2 12257*82 

-I,: 2fi IF < ISTI > 12258*82 

314 » §!4 12259*82 

iTP2- tl+2 1??fiO*fl? 

BEAD ( IEEAD ) I DX(I) , DI (I) , DZ (I) , 1=1, HP2 ) 12261*82 

WBITEJN2) ( Dili), hit). Mi). Z'T. &$2 f 12262*82 

IF ( ISLOP(ISTT) .EG. } &6 TO §80 2263*82 

NREAD = NSXL (ISTT) +NSYL(ISTT) ♦NSZL(ISTT) 12264*82 

IF ( NHEAD .EQ. ) GO TO 952 V ' 12265*82 

BEAD (IREAD ) < (H BXM (I , J) . W3TXH ( I, J) , HHIHJI, J) , HBTYS (I, J) , 12266*82 

JBZa I,J), HBTZa(I,J), J=1,f0), 1=2, 8P1 f 12267*82 

HRIIE (N2) (( HBXH I, J , gHTXH ijj J «Yfi(li5). WBTia(t.J), 12268*82 



2 * JdzHji/jn'fiBizHTijar/j^irion'fsitaprr 2257*32 

Maill (N2) (( HBXH I,J , HRTXH l',J K iBthtz'S). WBTia(t.J), 12268*82 

2 rnMTTHn „ tfBZH'l,j), HRTZmU,JJ, J-1.l0f/l-a f HP1 ) ' 12269*82 

332 CONTINUE 12270*82 

IF ( SODEIT .LE. -1 ) GO TO 954 12271*82 

IF (ELEMKT . EQ. SHEA2) GO TO 953 12272*82 

BEAD (IREAD) { ( (EPR1 S (I, J K) ,EPET1S ( I. J,K) ,EPB2S IT. J, K) , 12273*82 

2 EPST2S (I,J.K ,K=1 t aSSIfl1) , J=1,MNPCS(, 1=2. HP1 ) 12274*82 

HRITE (N2) ((( SPB1S(I.J,S)','EPBT1S(I,J,K), EPS2S (1 ,5, K) ' ' 2275*82 

2 tp , , n - , T , EP ^ 2S( S'^'^'^ 1 fi'l?"fl1)/5=1,aNPCS),'l=2 f !:P1 ) 12276*82 

IF ( aOD£l£ .EQ. GC TO 954 12277*82 

READ (iREAD) (( ( |„g i ,I,J „ RP3F T WIJKJ SIB^ |I a K| 12278*82 



349 



i ^ F ? <li&^fi K l * fI-BFT2 (I.J.K) „ K=1,MSSIH1 ), 12284*82 

* GO TO 95301 J " MH§CS 5 ' I = 2 ' Ap1 f fill:!! 

953 CONTINUE 159«7*fl? 

NHINGE = 1 123ftfi*fi3 

HEAD (IBEAD ) ( { (EPBl S (I, J, K) ,EPBT1 S ( I, J, K) , 12289*82 

2 ir ( no^\i^i s hl'^h*M s i' f=2 - flpi » flits 

BEAD (ifiEAD ) < ( (EPB F1 \ I, J, K) , EPBFT1 (I, J,K) , SLBF1 (I.J.K), 12294*82 

\. 5ITt ,„, , ,, SIBFT1 I.J.K . K=1.«skMl')i5=1,KNPcif;ii2iSpi) 12295*82 



E?BFT1(I,J,K) , SLBF1 (I,J,K), 
K=1.BSSIM1 ),J=1,BNPCS);i=2,BP1) 



95301 2 CONTINUE SLBFTl(l,J,KJ, K=1.Hs£lfl1 ) , J= 1 , HNPCS") , I = 2 ', HP1) 12297*82 

READ (IREAD ) ( ( (EPS MAI {1,1, Jj , EPSHIN (I.L.J) , EPSPEE (I, L, J) , 12299*82 

2 IF ( MODEIT .NE. = h^cVo'95V , '* Hi " fiE *' X " 2 ' MP1 > gjgfeB 
HEAD (ifiEAD ) (((YGROi 11.1.0). YTGBOS (I L, J) , J = 1.HHPCS ). 12304*82 

-bite ( N2 ) KcWoj'Jg £5, 'yIgIo '( 2, 1,. a . i, E npcs ), \mm 

954 2 CONTINUE L " 1 ' l)hls6E >» * = 2 <"*' > Iffi!! 

8 l5l a f A 2 2?g*i° ) S ° I0 958 |3 *§ 

DO 955 N = l!3 i?Tii*P9 

955 CONTINVE SEV(f ' N) = ° J 

958 HEIT ^lNal (KC[I3EV(I ' 8) ' N=1 ' 3) ' I=2 ' HP1 » » |;g 

ss i & 2°? 2 i T 2*jp E i - 1 > GC T0 98 ° I! t:fl 

DO 960 L = 1, NHINGE 12318*82 

DO 960 J = 1,MNPCS 12319*8? 

960 CONTINUE (I ' L ' J) = ° llllf^ll 

980 8fiI l OH |lN0i (( IHV < I ' L ' J »' J=1^HPCS), L=1, NHINGE), I=2,SP1 ) l|j| 2 *J 

1000 CONTINUE 1?l?u*09 

IF ( NTB .HE. ) GO TO 1020 12325*82 

.„„„ TOTTHE = TCTTHE + TIfiE 12326*82 

1020 CONTINUE 12327*fl? 

LI Y PEL = ITYPEL 12328*82 

ITYPEL = ITYPE 12329*82 

IHIwVi" " DTI 12330*82 

IABAN ■ 12331*82 

NJNC = 1?339*R9 

NTI1 = NTI + 1 l^lifl? 

, _ DO 1030 I = 1.NTI1 19T3U*R9 

10JO jp^g^ - ° 12335*82 

1040 JT = JT + 1 llii^tll 

IIHE = IIBE+DTI 1?11r*P? 

GO ^0*1046 * EC * PBINT " CE * AP80B ' EC * HEHBEfi > G0 T0 10< "» 1233 9*82 

1044 CONTINUE I7i2i*p9 

IF (JT .EQ. 1) PBINT 41 1234?*fl? 

FEINT 40,JT,TI8£ i51ttllfl5 

104o CONTINUE _ 12344*62 

NITF - 191U^*R9 

NIIERF = 1 123U6*R? 

IBDYN = 17^7.ft? 

I2VRSE= 1?TUR*R? 

1050 CONTINUE 1?1fltifl9 

IF ( IBVRSE .EQ. j GO TO 1060 12350*82 

in in A ?R2P - EQ " PRI " T - 0E - APR0B « E0 -- KEHBEE ) GO TO 1055 12351*82 

1055 CONTINUE l5$?5*fi? 

PRINT 195 12^u*R2 

1060 CONTINUE llllslll 

ITAPE = 1 193";fi*R9 

IF ( IRVBSE .BE. ) ITAPE = 12357*82 

1065 cL-Iinue pe - eq " ° » so io 107 ° liillxii 

If i It fflifcij 

1070 c-otJTTNTif" 12362*82 

1070 CONTINUE 12363*82 

g| I »5 12364*82 

gS I |3 12365*82 

"3 - »T 12366*82 

^n f - - n NITI 1 12367*82 

KCFFJ = 12368*82 

KCHECK = 12370*82 

IJDCi - 19T71ftflO 

IF ( ( ISSTEP(JI) i+IRDYN ) . NE. ) GO TO 1100 12372*82 

IF jNITEHF .NE. 1 GO TC 1100 12373*R? 

IF (JT ,|Q. J) GO TO 1100 12374*83 

NCHECK - 1 12375*83 

INDEX = 1 1?T7fi*R7 

1100 CONTINUE 1?377*H9 

IUVRSS = 1737R*R9 

COMMENT - SOLVE FOR JOINT REACTIONS 12379*82 



350 



COM* EST 
COMMENT 
C0H3SHI 
CA 



DO 1250 I = 1.NJT 

- SUBROUTINE IpiSl CALCULATES THE RESISTIVE SPBING FORCE AND 

- THE SPRING STIFFNESS FOE THE JOINT SPRINGS FOLLOWING 

- NONLINEAR LOADING , INELASTIC UNLOADING PATH 



1250 

COMMENT 
COMMENT 



1300 



COMMENT 
COMMENT 
COMMENT 
COMMENT 
COMMENT 



IF 



IF 



u L,Uftti4.ftta , AHKiaSilC . . . . . 

NELST (I,SJX,SJY,SJZ..SJV,SJXY,QJX,QJY,QJZ.QJV) 
ESE .N£. ) GO TO 1^50 



QJX 
QJY 
QJZ 
QJV 



LL II. 

( IEVfil_ 

RXX(I) = - SXX(I)*EXX(I 

RYYl.I = - SYY?l(*DYY{I 

RZZ I I ; = - SZZ (I) *DZZ(I 

HVV i,X = - SVV(I) *DVV(I 

KOJ |'li = KCFFJ 
(IMJ(I) ,EQ. 0) GO TC 1250 

NMJ = NMJ + 1 

KOMJ (NMJ,NITF) = KOFFJ 
CGNTINUE 
CALL SUBROUTINE DJSTSM 10 OETAIN THE SHEAH MOMENT AT EACH 

DO 1300 I = 1,NJT 

SHHC(I) =0.0 
IF (JST(I) .Eg. Of GO TC 1300 
CALL DJSTSMjI,STFJ,SH»OJ) 

IF (IEVHSE .NE. 0) GO TC 1300 

SHMO(I) = SHMOJ 
CONTINUE 

NITEEF = NITEHF + 1 
IF (iaVESE .NE. ) GO TO 1600 

COMPUTE FOB EACH JOINT - THE SUM OF APPLIED JOINT LOAD 
AND THE REACTION - WHEN THE APPROPRIATE EEflBER END FORCES 
ARE bUBTBACTED FROM THIS SUM THE RESULT IS THE JOINT 
EQUILIBRIUM ERRORS. FOR JOINT SHEAR OPTION SUETRACT ALSO THE 
££ E SI^ T S AT AB2 CARRIED BY THE JOINT SHEAR DEFORMATION. 
DO 1500 I = 1,NJT 



IF 



ERXX(I) = QXX(I) 
(DABS (QXX(I)) .GE. 

ERYY(I) = QYY(I) 
'"ABSJQYY(I) ) ,GE. 

EBZZjI) = CZZ(I) 



tX (II 



._) = CjYY(I) 
IF (DABSJQYY(I) ) .GE. 
ERZ21I) = CZZ (I) 
DABS(QZZ(IJ_) .GE. 1,02+15) 
(JST(l) .NE. 0) GO TO 1400 
EEVVYI) =0.0 



1400 



1500 

1600 

COMMENT 



IF (DABS 
IF 

GO T0"l56d 
CONTINUE 

ERVV (I) = 



1.0E+ .. 
♦ RYY(I 
1.0E+15 
+ EZZJI 



EBXX(I) = 0.0 

ERYY (I) =0.0 
- SHMO(I) 
EBZZ(I) =0.0 



iDABS(Q"yV(I)f .dE, 
CONTINUP 



IF 



swm 

155 



0E+ 



♦ SHMO (I) 
ERVV (I) =0.0 



CONTINUE 

INITIALISE THE FOLLOSING VECTORS USED II 

DO 1650 I = 1.NJT 



SUBROUTINE ADJTEE 



ERXXDN 

ERYYDN 
SBZZDN 
EBVVDN 
1650 CONTINUE 
REWIND N1 
REWIND N2 
REWIND N3 
REWIND Kit 

IF ( APROB , 
50 TO 1710 



.22. PRINT .OR. APROB . EQ. MEiJBEP ) GO TO 1700 



1700 
1710 






= 1, 



A NOW 



CCOHMEN'I 



COMMENT 

1850 

1900 

1950 
C0S5EKT 



CONTINUE 

PRINT 155, NI1F 

CONTINUE 

•IMES1? 

IFAE = 

NMNC 
DO 2000 JJ a 1,NB 

ISTT = 1ST (J J) 

LIT = LT(JJ) 

IMC(JJ) =0 

NITM (JJ)=0 
- SKIP FOR HULL MEMBER 
IF (ISTT.EQ.O)GC TO 1850 
CALL MEMSOL ( RM, RO, H, SI, LI. 13, 
IF (IflC (JJ) .EG. * 
GO TO 1950 

SET MEMBER END FORCE-MATRIX TO NULL BATBIX FOR NULL MEMBER 
do i you I — 1.6 

FOMS(JJ,I) = 0.0 
CONTINUE 
IF REVERSAL HAS BEEN SENSED AT THE BEGINNING OF 



L4. L6 ) 
NMNC + 1 



SS5SI&I " A m S S* l IH£ STEP l THEN SKIP STIFFNESS FORMATION CALCULATIONS 
COMgfiHT - AT THIS TIME STEP SINCE WRONG INCREMENTS HAVE ALFSDY BEEN 

- ADDED TO THE JOINT DISPLACEMENTS AT THE END OF LAST TIME STE 
SO EVERYTHING MUST BE EACKEE UP TO THE LAST TIKE STEP, COERE 
oTIif NESS MUST EE F02MED AT ITS END. REVISED INCREMENTS MUST 
Bfl ADDED TO JOINT DISPLACEMENTS, AND AGAIN THE NEXT TIME STE 

MUjT be begun. 

IF ( IRVRSE .NE. ) GC TO 2000 

IF (NMNC ,GT, ) PRINT 777 

IF SOLUTION FAILS FOR ANY REASON, 



COMMENT 
COMMENT 
COMMENT 

COMMENT 
COMMENT 



COMMENT 
COMMENT 

comsent 

COMMENT 

COHdENT 



THEN THE LAST COCD STORED 
SOLUTION ( NOT NECESSARIL Y""THE" LAST GOOD SOLUTION SCLVED~FOR ) 
IS READ AND RESULTS CUTFUT BEFORE PROCEEDING FURTHER ' 

i> ,i2 IljaE THINGS ARE DONE IN CASE OF FAILURE IN JOINT SOLUTION 
EITHER WITHIN THE TIME STEP OR AT A NEW TIKE STEP 
IF ( NMNC .EQ. ) GO TC 1955 
IABAN = 1 



12380*82 

12381*82 

12382*82 

12383*82 

12384*82 

12385*82 

12386*82 

12337*82 

12388*82 

12389*82 

12390*82 

12391*82 

12392*82 

12393*82 

12394*82 

12395*82 

12396*82 

12397*82 

12398*82 

12399*82 

12400*82 

12401*82 

12402*82 

12403*82 

12404*82 

12405*82 

12406*82 

12407*82 

12408*82 

12409*82 

12410*82 

12411*82 

12412*82 

12413*82 

12414*82 

12415*82 

12416*89 

12417*82 

12418*82 

12419*82 

12420*82 

12421*82 

12422*89 

12423*82 

12424*82 

12425*82 

12426*82 

12427*82 

12428*82 

12429*82 

12430*82 

12431*82 

12432*82 

12433*82 

12434*82 

12435*82 

12436*82 

12437*82 

12438*82 

12439*82 

12440*82 

12441*82 

12442*82 

12443*82 

12444*82 

12445*82 

12446*82 

12447*82 

12448*82 

12449*82 

12450*82 

12451*82 

12452*82 

12453*82 

12454*82 

12455*82 

12456*82 

12457*82 

12458*82 

12459*82 

12460*82 

12461*82 

12462*82 

12463*82 

12464*82 

12465*82 

12466*82 

12467*82 

12468*82 

12469*82 

12470*82 

12471*82 

12472*82 

12473*82 

12474*82 

12475*82 



351 



JEIST 92, JT, TIME 

' go fFihr - EQ - ! > G0 T0 1110 ° 

1955 CONTINUE 

INDEX = 
NCHECK = 
IF ( I5TT -EQ- ) GO TC 2000 
£ G 59 E ti^ " SUBROUTINE FORHST CALCULATES HEHBEE (6 X 6) STISFNFSS HATRTX 
COHhIbI - SBMTU S i N 1 A ? VANTAG£ CF SYMMETRY STORES iV CCHBACT VECTOH 
'CALL FOfiflST 



1960 
2000 

COKHENT 
COflSENT 



2005 



DO 1960*l"S"lJl HH ' EC ' *' SL ' S " HT ' L1 ' L3 ' L "' L6 ' JJ > 
SMC ( JJ ',!) = SHHT(I) 

CONTINUE 

If ( laVHSE . EQ. ) GO TO 2015 

?£SS!!L3H SiliSMSSSSI" 5 J0INT ««««»»"«. 

NITF = NITF - 1 
NITERF = NITERF - 1 
IRDYN = 1 
ISSTE? (JT) = 1 
JT = JT - 1 

TIHE = TIflE - DTI 
DO 2 005 I = 1.NJTT 

VELJI(I) = VELJT(I) - DVELJT(I) 

CONTI^ JTl15 = ACCJTtl ' * CACCJT M 

J = 
DO 2010 I = 1,NJT 

J = J + 1 

DXX(I) = DXX(I) - DELWJT(J) 

J = J + 1 

DYY(I) = DYY(I) - DELHJT(J) 

J — J + 1 



IF (JST 



DZZ(I) = DZZ(I) - DELWJT(J) 
ST (I) .NE. 0) 

dWjI) = o.o 



HE. 0) GO TO 2008 



2006 
2010 



GO TO 20T0' 
contJs1 ( ' ,+=1dVV(I) ' W"«CJ) 

GO TO 1050 
2015 CONTINUE 

coaasNT - DUMP OF stiffness mateix AND LOAD VECTOR. TO ACTIVATE SFT TA^T 
COMMENT - FIVE COLUMNS IN PROBLEM KUHBEB CAHD EQUAL TO PRINT ' 
IF ( APROE .SE. PRINT ) GO TO 2060 
DO A 



2040 



2050 
2060 



. 2050 JJ = 1,NM 
DO 2040 I = 1,6 

FOHTE3 (JJ,I) =0.0 
CONTINUE ' 

IS IT = 1ST (J J) 
I? (ISTT.EQ. 0)GC TO 2050 
PiUNT 99, ( S3C(JJ,I), 1=1,21), 
CONTINUE • i • 

CONTINUE 

DO 3 000 I = 1,NJT 
IF JNITF -GT. 1) GO TC 2900 



( FOaiEH(JJ,I) , 1=1,6 ) 



2900 



3000 



CALL DYSTLD ( 
FJXT 
FJYT 
FJZI 
FJVI 
CONTINUE 
EH XX 
EBYY (I 
ERZZ (I 
E2VV (I 
CONTINUE 

NCHECK 



FJX,FJY^FJZ,EJV,TIHE,I) 
I 



I) = 



FJX 
FJY 
FJZ 
FJV 

FJXT (I) 
FJYT (I) 
FJZT(I 
FJVT(I) 



♦ 2HXX(I) 
+ ERYY(I) 
+ ERZZfl) 
+ ERVV(I) 



= 



3010 
3020 



3030 
304 



3100 

3200 



3250 



INDEX = 
IF ( JT . GT. 1) GO TO 3200 
IF { ITYPE .EQ. 4 ) GO TO 3200 

DO 3 100 I = 1.NJT 

J = J + 1 
IF (ZHASSE(J) .GT. 1.0D-10) GO TO 3010 

ACCJT(J =0-0 
GO TO 3020 

ACCJT(J) = ERXX(I) /ZHASSR(J) 

IF (ZMASSE(J) .GT. 1.0D-10) GO TO 3030 
ACCJT(J) =0.0 



O TO 3040 

ACCJT(J) 
J = J + 1 
ACCJI(J^ =0.0 



ERYI (I) /ZMASSE(J) 



IF (JST (I) ".EC 
J = J + 1 
ACCJT(J) 

CONTINUE 

DO 3250 1=1 ,NJTT 



0) 50 TC 3100 

0. 



FACCJT (I) =ZHASSit(I)*ACCJT(I) 
FDAQJT (I )=CDAKF(I)*VELJT(I) 



CONTINUE 

J = 
DO 3300 1=1 , NJT 



12476*82 

12477*82 

12478*82 

12479*82 

12480*82 

12481*82 

12482*82 

12483*82 

12484*82 

12485*82 

12486*82 

12487*82 

12488*82 

12489*82 

12490*82 

12491*82 

12492*82 

12493*82 

12494*82 

12495*82 

12496*82 

12497*82 

12498*82 

12499*82 

12500*82 

12501*82 

12502*82 

12503*82 

12504*82 

12505*82 

12506*82 

12507*82 

12508*82 

12509*82 

12510*82 

12511*82 

12512*82 

12513*82 

12514*82 

12515*82 

12516*82 

12517*82 

12518*82 

12519*82 

12520*82 

12521*82 

12522*82 

12523*82 

12524*82 

12525*82 

12526*82 

12527*82 

12528*82 

12529*82 

12 53 0*82 

12531*82 

12532*82 

12533*82 

12534*82 

12535*82 

12536*82 

12537*82 

12538*82 

12539*82 

12540*82 

12541*82 

12542*82 

12543*82 

12544*82 

12545*82 

12546*82 

12547*82 

12548*82 

12549*82 

12550*82 

12551*82 

12552*82 

12553*82 

12554*82 

12555*82 

12556*82 

12557*82 

12558*82 

12559*82 

12560*82 

12561*82 

12562*82 

12563*82 

12564*82 

12565*82 

12566*82 

12567*82 

12558*82 

12569*82 

12570*82 

12571*82 



352 



ERXXU) = EfiXX(I) - FACCJTfJ) - FDAMJT(J) 12573*8^ 

IF(DAB5jFJXT(I)) .Gf.'l.00E+10)E3XX(I) = 0.3 ' 12574*82 



J = J ♦ 1 

EBXX (II = 

VB3 (FJXTm 

J = J + 1 



12574*82 

1 2 57^* ft? 

EHYY(I) = EBYY(I) - FACCJT(J) - FDABJT (J) 12576*82 

if(dabs_(f.M{I)) .si. i.00E*i0)ish(i) = oil 12577*82 

J - J + 1 12578*82 

EfiZZ(I) = ERZZ(I) - FACCJT(J) - FDAHJT(J) 12579*82 

IF DABS FJZT(I)) .GT. 1 .OOE + 10) EB2Z (I) = 0.0 12580*82 

IF (J flii , ,T? l,E 'n°), G ° TC 326 ° 12581*82 

GO TO^oT* = °- b 12582*82 

32b0 CONTINUE 12584*11 



J = J + 1 



12585*82 



EEVVJI) = EBVV(I) - FACCJT(J) - FDABJT (J) 12586*82 

3300 S«4?ftSI C * a " CI,J *^ T * 1 - 00E+1 °) £H¥V(I) = 5.6 12587*82 

DO 3400 I = 1.NJT 12589*82 

3 ?l iDABS(CXX{f)).LT.1.0E + 15.AHD.DABS(FJXT(I)).LT.1.0E*10) 12590*82 

<L GO TO JJ20 12591 + 8? 

,__„ ERXX(I) = EBXZDN(I) 12592*82 

3320 CONTINUE l ' l?sqT*fl? 

? Jl ]OABSlOXI(I)).LT.1.0Et15.AND.DABS(FJIT(I)).LT.1.0E+10) 12594*82 

X bU 10 JJJU 19^q^*fl? 

,,,„ ERYY(I) = EBYYDN(I) 12596*82 

3330 CONTINUE ' 1??q7*fl? 

i M ]S A §yP, Z2 ( i n-LX-1.0E*15.AND.DABS(FJZT(I)).I.T.1.0E+10) 12598*82 

ERZZ(I) = ESZZDN(I) 12600*82 

3340 CONTINUE V ' 12601*8? 

IF fJST(I) .EQ. 0) GO TC 3400 12602*82 

? }K iS a ^^ VV ( I ))' i 'T.1.0E*15-AND.DABS(FJVT(I)).I,T.1.0E+10) 12603*82 

Z (jJ TO J40U 1?f>0<Jl*R? 

3400 COKlISP™ = E2 ™W 12605*8^ 

COMMENT - ™ T = D 1 K08 H J E S2IIi lH|IJHB PA^IcaiAH TIg Bo |T|P BZI.G 12607*82 

C ACCESSED AGAIK THIS TIKE ONLY FOB THE PURPOSE OF 12609*82 

C (BACKED OP) STIFFNESS FCBHAIION 2610*82 

DO htiMK'^A J GC T ° 395 ° 12611*82 

DO 3700 I = 1,NJT 12612*82 

i 11 iDABSloXX(I))-LT.1.0B+15.AND-DABS(FJXT(I)).LT-1.0E*10) 12613*82 

rn In \%\\ 12614*82 

3510 CONTINDE 12616*8? 

JS1S ^n M )? AB ^ (£2XX(I)) ' GT - EfiE1 > G0 TC 5100 12617*82 

JOIj CONTINUE 12618*8? 

IF (DABS(QYY(I)).LT.1.0E*15.AND.DABS{FJYT(I)).LT.1.0E-H0) 12619*82 

2 GO ?8 l?38 12620*8? 

3520 CONTINUE 1?fi??*fi? 

3525 C^ffiI (£flyY(I)) * GT - EBB1) G ° T ° 510 ° ||:| 

; IES ]° A ?f« zz ( I ))- LT - 1 -0E+15.AND.DABS(FJZT(I)).LT.1.0E+10) 12625*82 

ro to ifti 12626*82 

3530 CONTINUE 35 lltlZ*!! 

3535 cM A Ng! (ESZZ(I)) - GT ' EHB2) G ° TC 510 ° llihi 

l\ lDABS(QVV(I)).LT.l.0E+15.AND.DABS{FJVT(I)).LT.1.0E+10) 12631*82 

rS In nnn 12632*82 

3540 CONTINUE 12634*e2 

3700 ^NTI DA NiI (£fi?V(I)) - GT ' EEE2) G ° T ° 510 ° Iff ji:8 

DC Jt^tt^-^LS? T0 3702 12637*88 

DO 3701 II = 1 KSHJ 12638*88 

I = KJ (II) 12639*88 

„ n< SHaJT(II,JT) = SHHO(I) 12640*88 

3701 CONTINUE 2641*88 

3702 CONTINUE 12642*88 
COMMENT - PRINT TABLE 8 IF REQUESTED 12643*82 
COMMENT - EVEN IF NOT REQUESTED, PRINT RESULTS FOR THE LAST TIME STEP 12644*82 

IF ( JT ,EU, Bin ) SO TO 3710 12645*82 

IF I IP8 .lb. ) GO TO 3860 12646*82 

„-- " i(JT-1)/IP8*IP8 .HE. JT-1) GO TO 3860 12647*82 

P'INT 11 12648*82 

m :Si;?!ji" 21II, -"- , - sl }W:i 

PRINT -234 12652*82 

RASTER = 12653*82 

TEMPXX = 0.0 12654*82 

TEMPYY = 0.0 2655*82 

TEMPZZ ■ 0.0 12656*82 

TEMPV7 = 0.0 2657*82 

DC 3850 I = 1,njt 12658*82 



SHMOJ = -SHMO(I) 2659*82 

IF (KGJ(I) .Ed. 1) GO TC 3800 12660*82 

um&miViBfflm-BffiP' dvv(i) - Eix(i) - syt(i) - ninii 

GO TO. 3840 nsfjttin 



3800 *i?*»8 - 1 12663*82 

■iaUL KA3T£:< = 1 1?6fitt*H? 

2 ?aiH Izz?lf hv$#t 1 hiiU J t tt ) '*&M Z1 * DVV ^>' *"(*>. EYY(I). 12665*82 

« l5sMlfi, fiY7 < r ) ' S ^SC(I), SHKOJ 12666*82 

CONiINOS 1?fifi7*H9 



384 



12667*82 



353 

2 IS |8 A §§|Jjl XX < I >>* <S;E »t- 0E+1 5« OB.DAES(FJXT(I)).GE. 1.0E+10) 12668*82 

oo, ^ TEMPXX = TEMPXX + BIX (I) 12670*82 

3842 CONTINUE V ' 12671*82 

? jtl IOA|5(Q3:y(I)).SI.1, 02+15. Ofi.DAES(FJYT(I)).GE. 1.0E+10) 12672*82 

^ IjU iU JoM 1?fi73*R? 

TEMPYI = TEMPS! + EYY(I) 12674*82 

3844 CONTINUE v ; I2675*fi2 

? }-r 1DABS(QZ2{I)).SE,1.0E+15. OH. D ABS (FJZT (I) ) . GE. 1 . OE+1 0) 12676*82 

3Sttfi rr«TTSP P2Z = 1EHP2Z * 8ZZ(I > 12678*82 

3S46 CGNTINUr. 12679*8? 

o £? 15 a BSiCVV(I)).GE.1-0E+15 .02. DABS (F JVT (I) ) . GE. 1 . 02+ 1 0) 12680*82 

3850 CONTINUE """ = ™ B ™ + ™™ Wftsk 

PRINT 237, TEBPXX, TEMPYY, 1EMPZZ, TEHPVV 12684*82 

3860 CONTINUE KASTEB - EC ' 1) PBIHT 154 llffcy 

IF I JT .ST. 1 ) GC TO 3865 12687*82 

PRIhFJ LTYPEL - NE> 9 > GC T0 3865 12688*82 

PfilNI 120, TIME 12690*8? 

PRINT 90°' ( VELJT ( I >' I = '•«« > 12691*82 

PRINT 130, TItE 12693*8? 

3865 PSIN ? N? Iki ACCJT(I, ' I= 1 ' NJTT > If!: 

REMIND N1 1?fiql*fl? 

REWIND N2 1ff!$?» 

NT = N1 

Nl = N2 



N2 = NT 



12697*82 
12698*82 
12699+82 



3870 CONTINUE" 12701*82 

spu " ] "BAN .EQ. ) GO TO 3890 12702*82 

HEAD (13) IREAD 12704*82 

REWIND IBEAD 12705*82 

1115 (III 1 ?} (DXX(I),DYY(I) ,D22(I),D7V(I) ,1=1, NJT) 12706*82 

DO 3880 I = 1.NJT 12708*82 

IF ( NTEHP .EQ. ) GO TO 3880 12710*82 
HEAD (IREAD ) IWRX (I. J) , BETE 1 1, J) ,WB X (I .J) ,BRTY (I, J) , SRZ II, J) , 12711*84 

JooU CONTINUE 1?71U*H? 

READ ( IREAD ) JT, TIME, ( VEIJT(I), I=1,NJTT ) 12715*82 

READ ( IREAD ) I ACCJT (I) , I=1,NJTT ) 12716*82 

ntt = htti 1 12717*82 

PRINT 96 "" " NTI1 " 1 WV&ll 

,_,, PRINT 18, JT, TIHE 12720*82 

3690 CONTINUE 1?7?l*q? 

COadEJT - 3U3B0UTINE PBIHT 9 OUTPUTS MEMBER BESUTS 12722*82 

3900 CAlI ' c ™^|^,NPROB, a fl,BO,«,SI,I1 / L3,I4,I.6, gjjjg 

IF ( IABAN .HE. ) GO TO 3950 12725*82 

IF ( JT .EQ. NTH') GC TO 3910 12726*82 

, IF ( I- 3 10 .EQ. ) GO IC 3950 1?727*82 

coaaewT - print table To if requested i2728*a? 

39io gg,^i ,)/iP,o * ipi ° - NE ' JI - 1) Gc to 395 ° mkll 

PBINI 11 1?7T1*ft? 

"IjiT 16.NPBOB, (AN2(II),II=1,9) 12732*82 

n'RINT 238 17773*P9 

DO 3940 I = 1,NJT 12734*8? 

3940 PRINT 235, I, EBXX(I), ERYY (I) , EBZZ(I), EHVV (I) 12735*82 

tfniisr yu i?77fi*fl? 

3950 CONTINUE 12717+82 

IF ( JT .EQ. BTI1 ) GO TO 10000 12738*82 

COMMENT - NEW TIME SIEP 12739*8? 

TI3E2 = TIKE + DTI 12740*82 

--„„„ „.""» = 4 »E« 12741*82 

HEWIND *1 12742*82 

S? - il 12743*82 

Stt = SS 12744*82 

N4 = NT 12745*8? 

REWIND N3 12746*82 

4?*,l-«. f ^ 12747*82 

NCHEcK = 12748*82 

INDEX = 12749+82 

DO 4000 JJ = 1,SH 12750*82 

12751*82 



1ST! = 1ST (JJ) 



LTT = LT (Jjj 12752*82 

IF { ISTT .EQ. ) Gb TO 4000 12753*82 

CALL FOfiMST ( EB, RC, K, SL, SiiMT, L1 , L3 , HI, L6, JJ ) 12754*82 

aLL DO°3970 ] -"l 6°' "' SL ' ?0HT ' L1 ' "' "' "» JJ ' 12755*82 

3970 rn«TTfn^ (JJ ' f) = F0MT (I) 12757*82 

Jy/U CONTINUE. 1?7 c ;p*fl'J 

4000 CONTINUE 12759*82 

«\ - 81 12760*82 

^ f ^2 12761*82 

N4 = NT 1?7P?*fi? 

IF ( APRQB .BE. PRINT ) GO TC 4060 12763*82 



354 



PEINT 98 

DO 4050 JJ = l.KH 

ISTT = IST(JJ) 
IF J ISXI .EQ. ) GO IC 4050 

CONTiNL SaC(JJ ' I) ' I=l ' 21) ' I F08H{JJ t I). 1=1.6 ) 



4050 

PRINT 98 
4060 CONTINUE 
DO 4200 I 

CALL 



1.NJT 



DFJXl(I) = fax - FJXT(lf 



4200 



IF 

DO 



4250 
4260 



4270 

coaaENT 

COMMENT 



4275 



CALL 
COKKENT - S 



DFJYT(I) = FJY - FJYtU) 

DFJZI(I) = FJZ - FJZT I) 

DFJVT(I) = FJV - PJVT(I) 
CONTINUE l ' 

IF (JT .SI. 1) GO TO 4260 
JNSMJ .EQ. G) GO TO 4260 
4250 II = 1,iiSHJ 

BJOINT = fij(II) 

114 = 11*4 

DISJI(II4-3,JT) = DXX (BJOINT) 

DISJT JlI4-2,JT) = DYY(HJOINT) 

DISJI(II4-1, JT) = DZZ(HJOINT) 
^„D*SJT II4 ' JT = DW HJOINT 
CONTINUE 
CONTINUE 

J = 
DO 4270 I = 1.NJT 

J ■ J ♦ 1 

AA = ACCJT (J) 

VV = VELJT<j[ 

*lll £${ *2. t^* (J) * (2.0*AA + VV*DSS1) + DFJXT (I, 

J = J + 1 

AA = ACCJT (J) 

VV = VELJT(J1 

*UUs'lj\ *L 0^f E (J) * <2.0*AA + VV*DSS1) +DFJYT (I) 
J = J + 1 

DFFS (3,1) = DFJZT(I) 
IF (JSTJI) . NE. 0) J = J + 1 
DFFS (4,1) = DFJVT(I) 
CONTINUE V ' 

- SET CONTROL CONSTANTS FCR FEAflE SOLOTION 

IHB = 4*IDJ + 3 

- CALCULATE THE NUHBEB OF DEGBEES OF FREEDOM 

DO 4275 I=1.NJT 

HL = 1 

JFSUE = 23 



GRIP2A (RH,20,W,SL,L3,L4,L6,IHB) 
IF ( IHB -LT. 16005 ) GC t6 4^80 
SYaBOLICAlLI HAKE NJNC = 1 

NJNC = 1 



NJNC 

IABAN = 1 
KTEJSP = JT + 
TEMP = IlflE 
NTEKP, TEKP 



1 

- + DTI 
PEINT 94. }~ 
GO TO 3870 
428 CONTINUE 

COHMENT - COHPUTE INCREMENTS OF VELOCITY AND ACCELERATION 

DVELJT(I)' = -2.0*VELJT(I) + 2.0*W(I)/DTI 
CONTIN0E CJT ' = - 2 -°* ACCJT ( I ) " 1 ».0*VELJ^(I)/DTI + 
DO 4400 I = 1,NJTT 

VELJI(I) = VELJT(I) * DVELJT 

ACCJT (ij = ACCJT (I) + CACCJT 

DELKJT(I) = H(I) 
CONTINOE 



4300 



4400 



DSS2*K (I) 



IB 



J = 
DO 4 500 I = 1,KJT 
J = J ♦ 1 
DXX (I) = DXX (I) 
J = J + 1 
DYY(I) = DYY(I) 
J = J + 1 



W'(J) 
W(J) 



DZZ (I) = DZZ (I) 
IF (JST (I) .NE. 0) 
(I) =0.0 



fc(J) 

GO TO 4410 



4410 
4500 



♦ 600 



DVV (I) 
GO TO 4500 

J = J + 1 

DVV (I) = DVV (I) + 

CONTINOE 

JTP1 = JT + 1 
(NSHJ ,EQ. 0) GO TO 46 10 
4 6 00 II = I.NSdJ 
tlJOINT = MJ(II) 
114 = 11*4 
DISJT (II4-3, JTP1 
DISJT (II4-2, JTP1 
DISJT (II4-1, JTP1 
DISJT 1X4 ,JTP1 

CONTINUE 



IF 
00 



W(J) 



= DXX(MJOINT) 
= DYI(MJCINT) 
= DZZ(HJCINT 
= DVV(KJCINT 



12764*82 

12765*82 

12766*82 

12767*82 

12768*82 

12769*82 

12770*82 

12771*82 

12772*82 

12773*82 

12774*82 

12775*82 

12776*82 

12777*82 

12778*82 

12779*82 

12780*88 

12781*88 

12782*82 

12733*82 

12784*82 

12785*82 

12786*82 

12787*82 

12788*82 

12789*82 

12790*82 

12791*82 

12792*82 

12793*82 

12794*82 

12795*87 

12796*87 

12797*82 

12798*82 

12799*82 

12800*87 

12801*87 

12802*82 

12803*83 

12804*82 

12805*83 

12806*82 

12807*82 

12808*82 

12809*82 

12810*82 

12811*82 

12812*82 

12813*82 

12814*82 

12815*82 

12816*82 

12817*82 

12818*82 

12819*82 

12820*82 

12821*82 

12822*82 

12823*82 

12824*82 

12825*82 

12826*82 

12827*82 

12828*82 

12829*82 

12830*82 

12831*82 

12832*82 

12833*82 

12834*82 

12835*82 

12 83 6*82 

12837*82 

12838*82 

12839*82 

12840*82 

12841*82 

12842*82 

12843*82 

12844*82 

12845*82 

12846*82 

12847*82 

12848*82 

12849*82 

12850*82 

12851*88 

12352*88 

12653*82 

12854*82 

12855*82 

12856*82 

12857*82 

12858*82 

12859*82 



355 



4610 CONTINUE 

GO TO 10 000 
5100 CONTINUE 

IF (JT . HE. 1) GO TO 5 110 
IABAN = 1 
PKINT 92, JT, TIHE 
PBINT 260 

GO TO 11100 
CONTINUE 
ITEHATE K1THIN TIME STEE 
ZESO DFFS - ONLY SOLVING FOE EBBOB 
DO 5150 I = 1,NJT 

DFFS(1,I) = 0.0 
DFFS (2,1 =0.0 
DFFS (3,1 = 0. 
DFFS(4,I) = 0.0 
CONTINUE 

DO 5155 JJ = 1,NM 
DO 5155 I = 1,6 

F0MM(JJ,IJ = 0.0 
CONTINUE 
SET CONTBCL CONSTANTS FOB FBABE SOLUTION 

IHB = 4*IDJ + 3 
CALCULATE THE NUMBEE OF DEGREES OF FBEEDOM 

NL = 3*NJT 
DO 5153 1=1, NJT 
IF jJST(I) .BE. 0) NL=NL+1 
CONTINUE 



5110 

CCKfiEST 
COMMENT 



5150 



5155 

COM SENT 

COMMENT 



5158 



ML = 1 

NFSUB 



23 



CALL G2IP2A (Kfl.BO , S, SL, L3 , 14 . L6 , IHB) 
IF ( IHB ,LT. 10000 ) GC TO §160 
:OMMENT - SYMBOLICALLY MAKE NJNC = 1 
NJNC = 1 
IABAN = 1 
P2IIJT 92, JT, TIME 

IF ( JT . EQ. 1 ) GO TO 11 100 
GO TO 3870 

CONTINUE 

DO 5200 I = 1,NJTT 

VELJT(I) = VELJT(I) + W (I) *2 
ACCJ1 I) ■ ACCJT I) + W 
CONTINUE 

J = 
DO 530O I = 1.NJT 
J = J + 1 

DXX (I) = DXX (I) + ii(J) 
J = J + 1 ' 



5160 



1200 



I) *DSS 



0/DTI 



DYY(I) = 
J = J + 



DYY(I) + W(J) 



5210 
5300 



DZZ (I) = D2Z (I) + SJ(J) 
IF (JST(I) .HE. 0) 50 TC 5210 
DVV(I) = 0.0 



5400 
D410 



W(J) 



= DXX(MJOINT) 

= DYY(MJOINT) 

= DZZ(HJOINT) 

= DVV(MJOINT) 



GO TO 53 

J = J + 1 
DVV(I) = DVV(I) 

CONTINUE 

IF TnSSJ .EQ. 0) GO TO 5410 
DO 5400 II = 1,NSMJ 
MJOINT = MJ(II) 
114 = 11*4 
DISJT(II4-3, JT 
DISJT[II4-2, JT 
DISJT(II4-1, JT 
DISJT(1I4 ,JT 
CONTINUE 
CONTINUE 

IF ( NITF .LT. MNITF ) GO TO 1065 
PRINT 20, MNITF 
COMHEN1 - SYMBOLICALLY MAKE NJNC = 1 
NJNC = 1 
IABAN = 1 
PBINT 92, JT, TIME 

IF ( JT .EQ, 1 ) GO TO 11100 
GO TO 3870 
10000 CONTINUE 

IF ( JT . LT. NTH ) GC TO 1040 

ANII1 = NTH 
IF { APACE .HE. SAVE 1 GO TO 10005 
WHITE (14,12) ( AN1(II), 11=1,40 ) 
100u5 CONTINUE 

IF /NSSa .22- 0) GO TO 10150 
DO 10100 II = 1,N3KM 
PBINT 205, HM(II) 

IF ( APSOB .KB. SAVE ) GO TO 10010 
WRITE (14,206) K2(II) 
10010 CONTINUE 

PRINT 2 10 
PKINT 2 12 

TEMP = TIME - ANTI1 * DTI 
DO 10020 J = 1.NTI1 

TEMP = TEMP + DTI 



Plit I HI 254, J,T.^F,FEMAXF II,J> ,FKHAXD (II, J) , FRMKCM (II , J) , 
FaMnCT(II.J) 
( APROB ,NE, SJVE ) GO i 
SalTE ( 14,255) SH (II) , J, TEMP, FRilAXF (II, J) ,FBMAXD (II, J) , 



IF 



1E,FEMAXF(II,J) ,FHMAXD (II, J) , FEMKCM (II , J) 
FSMHCT(II,J) ,I5MSHFJII,J) ,FBHLTD |ll# J) 
.HE. SJVE 1 GO TO 10020 



12860*82 

12861*82 

12362*82 

12863*83 

12864*83 

12865*83 

12866*88 

12867*83 

12868*83 

12869*82 

12870*82 

12871*82 

12872*82 

12873*82 

12874*82 

12875*82 

12876*82 

12877*82 

12878*82 

12879*82 

12880*82 

12881*82 

12882*82 

12883*82 

12884*82 

12885*82 

12886*82 

12887*82 

12888*82 

12889*82 

12890*82 

12891*82 

12892*82 

12893*82 

12894*82 

12895*82 

12896*82 

12897*82 

12898*82 

12899*82 

12900*82 

12901*82 

12902*82 

12903*82 

12904*82 

12905*82 

12906*82 

12907*82 

12908*82 

12909*82 

12910*82 

12911*82 

12912*82 

12913*82 

12914*82 

12915*82 

12916*82 

12917*88 

12918*88 

12919*82 

12920*82 

12921*82 

12922*82 

12923*82 

12924*82 

12925*82 

12926*82 

12927*82 

12928*82 

12929*82 

12930*82 

12931*82 

12932*82 

12933*82 

12934*82 

12935*82 

12936*82 

12937*82 

12938*88 

12939*88 

12940*88 

12941*88 

12942*88 

12943*88 

12944*88 

12945*88 

12946*88 

12947*88 

12948*88 

12949*88 

12950*88 

12951*88 

12952*88 

12953*88 

12954*88 

12955*88 



356 

10020 2 CONTIHD- FSKaCa l II ' J )' F£H aOT(II,J),FEHSHF(II,J),FHai.TD(II,J) 12956*88 

PEINT 205. Hi! (II) 12958*88 

IF ] iPBOE .{IE, SAVE ) GO TO 10022 2959*88 

10022 ralT &j!i*22 7) KH(II) 12960*88 

FEINT -11 12961*88 

PEINT 212 llli^Jlfl 

TEMP = TIME - ANTI1 * DTI 12964*88 

DO 10024 J = 1.OTI1 12965*88 

TEHP = TEMP + DTI 12966*88 

PEIKT 254, J,TEHP,ICAXFfII,J),TCAXD/II,J),TOHOH(ri,J), 12967*88 

2 TCROT(II,J) ,TCSHFJII,J) ,TOLTD(ll'j5 12968*88 

IF ( APEOE .NE. SAVE ) GO TO 10024 »l-"-.-i 12969*88 

MHITE (14,255) fiE(II),J,TESP,TOAXF(II,J),TOAXD(II,J), 12970*88 

10024 2 CONTINUE T0H ^ (^ ' J ) '^OT (II , J, ,TOS H F (II , J) ,Toi T D (II, J) 12971*88 

PRINT 220. HH(II) 12973*88 

I? 7 APKOE -NE. SAVE ) GO TC 10030 12974*88 

Iflfl^n rni-frfini ] HS (II) 12975*88 

luJJU CONTINUE 12<J76*fiR 

TEMP = TIME - ANTI1 * DTI 12977*88 

ISTT = 1ST (MB (II)) 12978*88 

t^TuSM?"' 11 ' ( ISTT > - E 0- StiEAB) GO TO 10060 12979*88 

5K|NT 251 . 12980*88 

DO 10050 J = 1,NTI1 12982*88 

TEMP = TEMP t DTI 2983*88 

PRINT 254, J,TEKP,FCBCEL(II,J),STRANL(II,J) , 12984*88 

2 „ BBOMNL II, J J.CUHVALJIlJj 12985*88 

IF I APEOE .BE. SAVE ) GO TO 10050 12986*88 

WRITE (to, 255) MB (II) , J, TEMP, FOECEL (II, J) ,STRANL (II, J) , 12987*88 

lOaSJ 2 rnllTTlm , BMOMNL(II,j5 ,CUBVAl|iI.J 12988*88 

lUJ^U CONTINUE 1?9R<? + flfl 

PRINT 220. MM (II) 12990*83 

IP 7 APROt ,JjE. SAVE J GO TO 10052 12991*88 

inns? " HIT rni^TT5 2 ,- 2) ^f 11 ) 12992*88 

10052 CONTINUE 12991*88 

OBT „_ ,„ TEap = TIHE " ANTI1 * DT * 12994*88 

Hill 252 12995*88 

ps "J n 2 30 12996*88 

DO 10054 J = 1.BXI1 12997*88 

TEHP = TEMP + DTI 12998*88 

PRINT 254, J,TEMP,FORCER(II,J) , STBANR (II, J) , 12999*88 

2 BBOHNB(II,J ,CURVAB(II,Jj 13000*88 

IF f APROE .ME. SAVE ) SO TC 10054 3001*88 

WRITE (15,255) KM (II) , J, TEMP, FORCER (II, J) , STEANS (II, J) , 13002*88 

2 BMCMNR(II,JJ ,CUEVAE(II,J) 13003*88 

10054 CONTINUE „ 13004*88 

GO TO 10100 13005*88 

10060 CONTINUE 13006*88 

PEINT 251 13007*88 

PRINT 253 13008*88 

DO 10070 J = 1.NTI1 13009*88 

TEMP = TEMP + DTI 13010*88 

PRINT 254, J, TEMP, FOECEL (II, J) ,STBANL ( II , J) , 13011*88 

2 B BOH ML (II, J) .CU5VAL (II, Ji , SHFOBL (II,J) , GAKMAL ( II,J) 13012*88 

IF (APHOB .ME. SAVE) GO TO 10070 13013*88 

iiBITE (15,255) MM (II) , J , TEMP, FOECEL (II .J) .STBANL (II . J) , 13014*88 

2 BKGMNL(II,J),COEVAL(II,J),SHFCEL(II,J) , GAMMAI (II, J) 13015*88 

10070 CONTINUE 13016*88 

PEIiiT 220, MM(II) 13017*88 

IF ( APflOE .ME. SAVE ) GO TC 10072 13018+88 

BP.ITE (15,222) BH (II) 13019*88 

10072 CONTINUE 13020*88 

TEMP = TIME - ANTI1 * DTI 13021*88 

PRINT 252 13022*88 

PRINT 253 13023*88 

DO 10080 J = 1,NTI1 13024*88 

TEIiP = TEMP + DTI 13025*88 

PRINT 254, J,TSMP,FCRCER(II,J) .ST5ANB (II.J) , 1302t>*88 

2 BMOMftK(II,J),CURVAR(II,J1 ,SHFOHB( II,J) , SAHMAE (II, J) 13027*88 

IF (APROB . NE. SAVE) GO TO 10080 13028*88 

WRITE (15,255) BM (II) , J, TEMP, FOBCERJII, J) .STEAHP. (II ,J) , 13029*88 

2 BMOMNfi(II,J) ,CURVAfi(II,J) ,SHFORB ( II, J) ,GAMBAB(II, J) 13030*88 

10080 CONTINUE 13031*88 

10100 CONTINUE 13032*82 

10150 CONTINUE 13033*82 

PRINT 11 13034*82 

PRINT 110, TIKE 13035*82 

PRINT 100, ( DXX(I), DIY(I), DZZ(I), DVV(I), 1= 1 , NJT ) 13036*82 

PEINT 90 13037*82 

PRINT 120. TIME 13038*82 

J = 13039*82 

DO 10160 I = 1,NJT 13040*82 

J = J + 1 13041*82 

VV1 = VEIJT(J) 13042*82 

J = J + 1 13043*82 

VV2 = VELJT(J) 13044*82 

J = J + 1 13045*82 

VV3 = VELJT(J) 13046*82 

IF (JST(I) -HE. 0) GC TC 10158 13047*82 

VV4 =0.0 13048*82 

GO TO 10159 13049*82 

10158 J = J + 1 13050*82 

VV4 = VELJT(J) 13051*82 



357 



10139 CONTINUE 
_„ , PfilKT lOff, VV1,VV2,VV3,VV4 
10160 CONTINUE 
PHI NT 90 
PRINT 130, time 
5=0 
DO 10170 I = 1,{JJT 
J = J + 1 
AA1 = ACCJT(J) 
J = J + 1 
AA2 = ACCJT(J) 
J = J + 1 
AA3 = ACCJT(J) 
IF (JST(I) .KE, 0) GO TO 10168 

AA4 =0.0 
GO TO 10169 

10168 J = J + 1 
, n , rr AA4 = ACCJT(J) 

10169 CONTINUE 

PRINT 100, AA1,AA2,AA3„AA4 

10170 CONTINUE 

IF (NSMJ ,£Q, 0) GO TO 11000 
DO 10600 II = 1,NSHJ 

I = BJ(II) 

114 = 11*4 
DO 1020 J = 1.NTI1 
IF ( II .EQ. 1[ GO TO 10190 
IF (HJO - T) 10190,10180,10175 



10175 

10180 

10190 
10200 



10270 

10280 

10290 
10300 



GO TO "1(32 DO" 

GO To'lrf&o" DISJT « II1 - 3 ' J ) " DISJT (1. J) 



iJ) = DISJT{II4-3,J) - DISJT(II4-7,J) 



TB (J) = DISJT(II4-3,J) 
CONTINUE ' 

CALL CSPLOT (IE, 1 , I, TIHE, II) 

DO 10300 J = 1,NTI1 
IF (II . EQ. |f GO TO_10290 



IF (HJO 
TR 

GO TO 1(J3 
TH (J 

GO TO 103 
T 

CO NT IN 



1) 10290,10280,10270 
T ^L" DISJT(II4-2,J) " DISJT(II4-6,J) 

THJJ) = DISJT(II4-2,J) - DISJT(2,J) 



THjJ) = DISJT(II4-2,J) 



CA^L CSPLOT (TB,2,I,TIHE,II) 

DO 10400 J = 1,NTI1 

(II .EQ. 1l_GQ TO 1Q390 



10370 
10380 

10390 

10400 



" (HJO - Y) 10390,103867 10370 

O T !d400 = DISJT < IIit -''' J > " DISJT(II4-5,J) 



10470 

10480 

10490 
10500 

10 520 



10530 
10540 
10600 
1 IOuO 



1 1 100 



GO Tt 

TH(J) = DISJT (II4-1 # J) - DISJT(3,J) 
GO TO 10400 * * ' 

TS(J) = DISJT(II4-1, J) 
CONTINUE 

CALL CSPLOT (TH ,3,I,TIME, II) 

DO 1050 J = 1.NTI1 
IF ( II .EQ. 1) GO TO 104 90 
IF (HJO - T) 10490,10480,10470 
GO To'^CsV 01& "<l"'rf - DISJT(II4-4,J) 
GO TO L 1^D0 = 0X2J tUI*.V ~ DISJT(4,J) 

Ts]j) = DISJT (114, J) 
CONTINUE 
CALL CSPLOT (TH ,4 , I,TIH£, II) 
DO 10520 J = 1.NTI1 

TH(J) = SHHJT(II,J) 
CONTINUE 
CALL CSPLOT (TE, 5, I, TIME, II) 

IF ( APEOF -NE. SAVE ) GO TC 10540 
WRITE (16,256) HJ(II) 

TEHP = TIB! - ANTI1 * DTI 
DO 10 530 J = 1,NTI1 

TEHP = TEHP + DTI 
WHITE (16,257) HJ (II) , J, TEHP, DISJT (II 4- 3, J) , DIS JT (II4-2, J) , 
! DISJT{II4-1,J) ,DISJT(II4,J) ,SHHJT (Il'j 

CONTINUE ' ' 

CONTINUE 
CONTINUE 
CONTINUE 

IF ( IABAN .EQ. 1 ) NTR = NTE + 1 
IF ( IABAN .EQ. ) GO TO 11100 

IF ( NTE .EC. .01. NTE .61. NTEA ) GO TC 11100 
DTI = DTI * 0.5 
TEHP = ( TCTTME - TIME ) / DTI 
NTI = IfiHP 
ITYPE = 4 
PSINT 200 
GO TO 900 

CONTINUE 
EETUKN 
END 



13054*82 

13055*82 

13056*82 

13057*82 

13058*82 

13059*82 

13060*82 

13061*82 

13062*82 

13063*82 

13064*82 

13065*82 

13066*82 

13067*82 

13068*82 

13069*82 

13070*82 

13071*82 

13072*82 

13073*88 

13074*88 

13075*88 

13076*82 

13077*82 

13078*82 

13079*82 

13080*82 

13081*82 

13082*82 

13083*82 

13084*82 

13085*82 

13086*82 

13087*82 

13088*82 

13089*82 

13090*82 

13091*82 

13092*86 

13093*82 

13094*82 

13095*82 

13096*82 

13097*82 

13098*82 

13099*82 

13100*82 

13101*82 

13102*86 

13103*82 

13104*82 

13105*82 

13106*82 

13107*82 

13108*82 

13109*82 

131 10*82 

13111*82 

13112*86 

13113*82 

131 14*82 

13115*82 

13116*82 

13117*88 

131 18*88 

13119*88 

13120*88 

13121*88 

13122*88 

13123*88 

13124*88 

13125*88 

13126*88 

13127*88 

13128*88 

13129*88 

13130*82 

13131*82 

13132*82 

13133*82 

13134*82 

13135*82 

13136*82 

13137*82 

13138*82 

13139+82 

13140*82 

13141*82 

13142*82 

13143*82 



358 

rH!«i SS »«»»*IS5x3S*J3TB:?lSf** S0BBODTI1IB ««***«•«..*.«««.««„.;« 
/^"O^BALAoi/ ^I(|5) .|gS S C25).HLJ(25 J .HHJC25) # VIJ( 2 5,.TOa(25). jljigli 

common /Biocio/ ss£h#?«L If J§S*f3 

CCHHOK /SLOC21/ ACCJT Y1QQ) ,VELJT{100) -ZMASSH MOO) .DACCJTMOO) 111SU*RS 

2 COMOH/ilC/ ggl H|i EBl ,,EH2.D«.CH.ITI.M(2<» , H J(20) ,««,, ||gjl 

DSS2=4.0/DTI**2 iqifq*ft7 

DSS12=2.6/DTI 13lfi0*ft7 

DO 100 I = 1,JTN lllfjill 

IF (JST(I) .HE. 0) J = J ♦ 1 lllfililo 

U ioTf J I\i! s - 0) IL= * JlillJfl 

DO 300 I = 1,11 ioi-7?.|Z 

300 HETOBH FSS(I) = PSS tD * DFH(I.J», IJgg 

Fjjr) I J 1 / J*H2 

iaJJ 13174*82 



APPENDIX G 
SAMPLE INPUT 



f|*»PLE 8,4 - CANTILKVEEgC BEAM H 14X142 WITH DYNAMIC LOAD 3CTT NO BASS, 
AT TH L£8EE END. JSYES OPTION AND NONLINEAR STRESS-STRAIN C3R7E FOR j6l1T. 
1PDNO JSYES LOAD INCREMENT (STATIC) 

2 5 2 2 2 2 l 

? .„„ 1 0-0 0.0 0.001 

1 100.0 0.0 2 

2 

2 

1 1 

1 15 ■ 6, 84 6 84 680 

1 3 1 0' 2078 3013 

0.01 0.000001 o 1807 7228 



1 



1 

1 10 2 



1.00E+20 1.00E+20 1.00E+20 

2 0,0 

11500,0 2 °8?58°'° SHEAfi 1660.0 41.54 1 1 

10 400.001 0.01 0.01 2 1 

100,0001 0,001 1 i 

1PDNO JSYES 2ND LOAD INCREMENT (DYNAMIC) 

3 1 1 1 1 1 111 
10 10 10 



1 



12 

2 1.0 0.1 

1 4 -40 40 

13 4 



EXAMPLE 9,2 - BERKELEY 1-EAY 3-5TOHY FRAME OF R.B.CLOUGH AND D T TANG- 
JOINT 5 MEMBER SHEARS ARE INCLUDED; EC400-I EARTHQUAKE: * 

921 JSYES STATIC ANALYSIS saV E 

6 a 2 9 8 n n ° °„ „ ° ° 6 9 „ 12 12 2 
8 1 0.0 0.0 0.001 

1 144,0 0.0 2 

1 0.0 80.0 3 

3 0,0 64.0 5 7 

2 0.0 80.0 4 

2 4 0,0 64,0 6 8 

1 2 

1 3 4 5 6 7 8 

1 2.3005 2.3005 2.8735 2.8735 0.246 1 

n i ' , 3 n„ r.i ° 255 472 

0.1 1.0E-05 219 1314 

1 10 3 

3 2 5 7 

2 10 4 

<* 2 6 8 

3 3 1 4 
5 3 2 6 

7 3 3 8 



1 

2 

3 

4 0.006011 



1.0E+20 1.0E+20 1.0E+20 1.0E+20 

1.0E+20 1.0E+20 1.0E+20 1.0E+20 



0,006011 
0. 006009 
0.006009 



8 0.006017 

1 10 SHEAR , -, , 0.006017 

1 1 ill 

2 8 SHEAR 

1 1 

3 16 SHEAR 



2 2 

1 3 



1 1 1 

1 1 1 



«0*?06 HiZ 3'2 005 IS', 1 1.OB-0SO.0 

4U.^4fa 4.234 0.0 20 1 1 flF-n^i n 

|5.00 3 0.367 -2.3005 10.1 KOE-OSOro 

'ici'VA HSS 2 '2 735 30 ' 1 1.0E-050.0 

40.243 5.463 0.0 40 1 1 nv-n^i n 

24,316 0.284 -2.8735 35, hoI-oi^O 



o 



60 



361 



11460.0 ° 134 1970 5910 

2 4 1 

11650, 



441 441 650 
146 2700 7050 



1 1850. 
1 1880.0 



392 392 636 

127 1520 4840 

496 496 675 

161 2450 6120 



1 



0-0 139.399 -0.00441 

45.6995 45.6995 -2l015 

93.6995 93.6995 -2.015 

0-0 139.399 -0.00426 

45.6995 45.6995 -2. 025 

93.6995 93.6995 -2^025 

0.0 139.399 -0.00380 

45.6995 45.6995 -2.06 

93.6995 93.6995 -2.06 

1 10 200,01 0.1 0.012 

■042 1 100.001 0.01 

5 6 7 8 9 



922 JSIES DTNAHIC AKALISIS - EC400-I INPOT SSVF 

,8 ,i ,3 1 1 ' » i i ' i 1 1 i 1 "" 



i 



-1. 08+20 



560 



-1. 0E+2Q 

1 3.864S+18 0,001 1 

2 3.8642*18 ol 001 1 
1 218 112 66 -448 736 -163 34 1 -118 413 -454 -93 

-442 -33 332 -464 420 -70 182 -631 323 -427 423 -743 526 -442 345 -818 

498 -835 520 -774 609 -508 547 -592 793 -54 600 -558 673 -530 790 -743 

776 -799 806 -749 770 -608 866 -600 875 -636 970 -583 758 -577 458 -74S 

969 -979 910 -272 105 -750 789 -415 509 -388 -515 -119 -710 455-1234 194 

-484 723 1537 -437 -590-1249 -435 -566 -126 -388 1872 3278 1280 2730 402 1479 

-1045-5349-3461-1594-1704 1721 3675 425-3592 3653-726 1084 896 -474 645-2385 

31?I 22!~ 2 §g| 80 ^-^T§ Til? 538-2227 2604-1236 3397-980 402-1055-1405 1230 

-3115 641 -258 467 1018-1592 -492-721 3157 -243 2745 1320-3618 2048-4096 439 

-858 45 93 218b -6b4 -62 -497 -184-2939 1616 -709 1501-2009 -925-1739 

545 574 603 633 699 743 802 817 898 935 994 lolo 1097 i?52 i$i?§ AU 

1295 1332 1391 1428 1494 1538 1590 1627 1685 1752 1781 832 1884 1971 1QS7 5ni7 

2090 2134 2193 2230 2289 2340 2392 2443 2502 2546 2598 2664 2701 2753 2797 llll 

^900 2966 3010 3062 3121 3143 3194 3231 330S 3341 3459 3503 3547 3621 VAl 3717 

3753 3790 3834 3864 3937 3930 4018 4085 4129 4217 426 1 4283 434? 43Rft iIu3Q link 

SIS8 1192 U637 4666 "40 "84 «857 4945 5005 5093 5174 5225 5277 5343 540? %l%l 

l\il Wit M\ 1%!% VAl \\n §121 I" 9 6006 ml iUo i^i till llll llli ISI* 

6550 6616 666 1 6712 6778 6845 6896 6948 7073 7146 7205 7793 7330 7iin3 nlai. t£qq 
7676 7735 7794 7868 7919 7963 8007 8066 8125 8206 8294 8361 8434 8471 8493 8537 
860U 8670 8707 8773 8832 8920 9008 9052 9126 9170 9207 925 9295 9347 9391 till 
9509 9590 9641 9730 9788 9847 9906 99871 0009 100751 01421 0193 10259 10 3 tfi in III i 037n 
103991042910480105471060510 6 72107011075310819109071098111025 11^ 
112751 13 1211363114301146611533115351 159211650117021 17981 18491 19231 194512000 



APPENDIX H 
SAMPLE OUTPUT 



9B 



KQ 

O 

to 
He 

ou 

OK 



H I 



Hen 

at as 



«c 
rao 

M 

OH 

CCO 
Bfl 

>tn 

HW 

BE 
< • 

rw 

OK 



04 = 

=:h 



363 



364 



;eo 



HIS 
UV] 

i= 

uto 

-JO 

CbO 
L5 H 

H3Qi 
Q O 

»JOQ 

wi-JO 

woo* 



UHQ 



V)-J<< 



=o 

OS 



cuO 

CUOO- 

Q0=O 

C* 

^ tn 

a: w 
o 

WJI 
QO< 

M 

UJN 

tntosa 

MH3 

►jo 
x w 

W6— 4 



Ha 
rau 

OB 

■CM 

o* 

"J to 

e- 
UW 

Ml 

r:w 
-em 

=5W 

MM 

CSH 



O 6-4 

oco 



E4D4 

MVJ 

HI 






5= 

N 



UH 
Ihffi 

oo 

BbS 

OS W fMlfirNNNOOOONOOOON 
HQm 

a uas 
sou 



^D5t0 OOOOOOOOOOOOOOO 



o 
a, a* 



-3 


C O 


a 


o z 


-c 


»1C 


H 


feutt 




-J 


H 


«soo 


o 


HO » 


a. 


oCDGlQ 


z: 


00*62 


t-^ 


>* 




OH 




1 IWl II 




o« 




aj- 








W« 




-jcq 




mQ 






Q* II 

H 
BO 

o 



UK 
■303 

rod coorj> 
<c — 

H=3 



365 



u 

H 






o 


o 




II ^ 


6-t 




w o 


S 


e- 


5S 


a. 


Eq 


s 


« 


C3M 


H 


b* 


fc.O 




py 


^ 




o 


SS 




1 


HWlfl 




M 


MM 






to 






HE*" 






S3 SB (J 






HH2 






oo< 






n^oj 






u 




BW 


U*W J 




OS 


QUO 




MM 


= H 




GuO 


05 (U 




"3 


IWWH 






OU=E 






E&.M 






3WO 






asw^ 







B H — (sg 



366 



DO 

oo 



t.m 




OH 




EZ 


r-tr- 


CAU-*. 


!->>£> 


»SEO 


f-ivo 




<->io 


KM 


\o»e 


wou 


*o^ 


ucn 


f~<N 



til 

o 



■* «- (M 



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APPENDIX I 
DIGITIZED VALUES OF EARTHQUAKE MOTIONS EL CENTRO 1940 AND EC400-I 



EL CEHTEO EAfiTHQOAKE:- NtJHBEE 01 
ACCELERATION AXIS HULTIELIER = C 



POINTS = 1 00; 
.0001 TIMES G; TIHE AXIS HULTIPLIEE = 0,001 SEC, 



ACCELEBATION 






108 


10 


159 


-1 


189 


1 


59 


-12 


200 


-237 


76 


425 


94 


138 


-88 


-256 


-387 


-568 


-232 


-3 43 


-402 


-603 


-789 


-666 


-381 


-429 


897 


-1696 


-328 


-828 


-945 


-885- 


-1080- 


■1280 


1144 


2355 


1428 


1777- 


•2610- 


-3194 


2952 


2634- 


2984 


54 


28 65 


-469 


1516 


2077 


1087 


-3 25 


1033 


-803 


520- 


■1547 


65- 


■2060 


1927 


-937 


1708 


-359 


365 


-736 


311- 


•1833 


227 


-435 


216- 


■1972- 


-1762 


146 


-47 


2572- 


■2045 


608- 


•2733 


1779 


301 


2183 


267 


1252 


1290 


1089 


-239 


1723- 


-1021 


141- 


1949 


-242 


-50 


-275 


-573 


-327 


216 


108 


235 


-669 


14 


493 


149 


-200 
















TIHE 













42 


97 


161 


221 


263 


291 


332 


374 


429 


471 


581 


623 


665 


720 


750 


789 


830 


872 


906 


941 


963 


997 


1066 


1075 


1094 


1168 


1315 


1384 


14 12 


1440 


1481 


1509 


15 37 


1628 


1703 


1800 


1855 


1924 


2007 


2215 


2270 


2320 


2395 


2450 


2519 


2575 


2652 


2708 


2769 


2893 


2976 


3 068 


3129 


3212 


3250 


3386 


3419 


3530 


3599 


3668 


37 3 8 


3835 


3904 


4014 


4056 


4106 


4222 


4314 


4416 


4471 


4618 


4665 


4756 


4831 


1970 


5039 


5108 


5199 


5233 


5302 


5330 


5 343 


54 5 4 


5510 


5606 


5690 


5773 


5800 


5309 


5869 


5883 


5925 


5980 


6013 


6085 


6132 


6174 


6188 


6189 

















EC400-I EARTHQUAKE:- NUHBEH OF POINTS =218; 

ACCELEEATION AXIS HULTIPLIES = 0,0001 TI8ES G; TIHE AXIS HULTIPLIEE 



0,001 SEC. 



ACCEL 

-442 

498 

776 

969 

-484 

-1045 

75 

-3115 

1618 

1479 

1038 

-402 

-858 

TIME 

545 

1295 

2090 

2900 

3753 

4548 

5520 

6550 

7676 



EEATION 



33 

-885 

-799 

-979 

723 

-5349- 



332 

520 

806 

910 

1537 

3461 



448-2603 



641 

280 

-474 

-920 

-317 

45 

574 
1332 
2134 
2966 
3790 
4607 
5579 
6616 
7735 



-258 
2543 
1479- 
-243 
624- 
93 

603 
1391 
2193 
30 10 
3834 
4637 
5638 
6661 
7794 



-464 
-774 
-749 
-272 
-437 
1594- 
800- 
467 
-594 
1968 
-51 1 
1619 
2186 

633 
1428 
2 230 
3062 
3864 
4666 
5696 
6712 
7868 



420 

609 

770 

105 

-590- 

1704 

1878 

1018 

637 

1565 

1636 

1274 

-664 

699 
1494 
2289 
3121 
3937 
4740 
5763 
6778 
7919 



112 

-70 

-508 

-608 

-750 

-1249 

1721 

-910 

-1592 

45 

-587 

-1068 

-1077 

-62 



743 

1538 

2340 

3143 

3930 

4784 

5807 

6845 

7963 



66 
182 
547 
866 
789 
-435 
3675 
533- 
-492- 
5 07- 
1452- 
1 145- 
1007 
-497 
110 
802 
1590 
2392 
3194 
4018 
4857 
5 873 
6896 
8007 



-448 
-631 
-592 
-600 
-415 
-566 
4 25- 
2227 
1721 
2082 
1358 
1955 
1466 
-184- 
169 
817 
1627 
2443 
3231 
4085 
4945 
5939 
6948 
8066 



736 

323 

793 

875 

509 

-126 

3592 

2604- 

3157 

1497- 

1559 

303 

-665 

2939 

213 

898 

1685 

2502 

3305 

4129 

5005 

60 06 

7073 

8125 



-163 
-427 
-541 
-636 
-388 
-388 
3653- 
123 6 
-243 
2694 
-616 
936- 
1506 
1616 
258 
935 
1752 
2546 
3341 
4217 
5093 
6108 
7146 
8206 



341 

423 

600 

970 

-515 

187 2 

1726 

3397- 

2745 

841- 

195 

1527 

-580 

-709 

309 

994 

1781 

2598 

3459 

4261 

5174 

6190 

7205 

8294 



-118 
-743 

-558 
-583 
-119 
3278 
1084 
1980 
1320 
3417 
-4 
1082 

890 
1501 

361 
1030 
1832 
2664 
3503 
4233 
5225 
6248 
7293 
8361 



413 

526 

673 

758 

-710 

1280 

1896 

140 2- 

■3618 

403 

587 

•1645 

-580 

■2009 

405 

1097 

1884 

270 1 

3547 

4342 

5277 

6322 

7330 

8434 



-454 
-442 
-530 
-577 

455- 
2730 
-474 
10 55- 
2048- 
-694 
-425 

502 

-74 
-925- 

442 
1126 
1921 
2753 
3621 
4386 
53 43 
6366 
7403 
8471 



-93 

345 

790 

458 

1234 

402 

645- 

1405 

4096 

-57 

1460- 

280 

-951 

1739 

478 

1207 

1987 

2797 

3658 

4438 

5402 

6425 

7485 

8493 



560 
-818 
-743 
-745 

194 
1479 
23 85 
1230 
1439 
-562 
1594 

521 

191 

493 
1229 
2017 
2863 
3717 
4504 
5454 
6491 
7588 
8537 



8604 8670 8707 8773 8832 8920 9008 9052 9126 9170 9207 9251 9295 9347 9391 9465 
9509 9590 9641 9 730 9788 9847 9906 9987100091007510 14210193102591031810340103^ 
103991042910480105471060510 67210701107531081910907 0981 11025 110691 1121 1157 1209 
11275113 12113631143011466115331155511592116 501170211798118491192 31 94512000 



411 



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414 



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University of Florida, Gainesville, Florida, March 1978. 

48. Santhanam, T.K., "Model for Mild Steel in Inelastic Frame 
Analysis," Journal of the Structural Division, ASCE, Vol. 105, No. 
ST1, January, 1979, pp. 199-220. 

49. Sechler, E.E., Elasticity in Engineering , Dover Publications, Inc., 
New York, 1968. 

50. Sheinman, I., "Large Deflection of Curved Beam with Shear 
Deformation," Journal of the Engineering Mechanics Division, ASCE, 
Vol. 108, No. EM4, August, 1982, pp. 636-647. 

51. Tang, D.T., and Clough, R.W., "Shaking Table Earthquake Response of 
Steel Frame," Journal of the Structural Division, ASCE, Vol. 105, 
No. ST1, January, 1979, pp. 221-243. 

52. Tankersley, D.F., and Dawkins, W.P., "A Discrete-Element Method of 
Analysis for Combined Bending and Shear Deformation of a Beam," 
Research Report 56-12, Center for Highway Research, The University 
of Texas, Austin, December, 1969. 



416 



53. Timoshenko, S.P., and Gere, J.E., Theory of Elastic Stability , 
Second Edition, McGraw-Hill, New York, 1961. 

54. Timoshenko, S.P., and Young, D.H., Elements of Strength of 
Materials , Fifth Edition, Litton Educational Publishing, Inc., New 
York, 1968. 

55. Workman G.H., "The Inelastic Behavior of Multi -Story Braced Frame 
Structures Subjected to Earthquake Excitation," University of 
Michigan Research Report, September, 1969. 

56. Zienkiewicz, O.C., The Finite Element Method, Third Edition, 
McGraw-Hill, London, UK, 1977. : 



ADDITIONAL REFERENCES 



1. Manual of Steel Construction, Eighth Edition, American Institute of 
Steel Construction, Inc., Chicago, Illinois, 1980. 

2. Przemieniecki , J.S., Theory of Matrix Structural Analysis , McGraw- 
Hill, New York, 1968. 



417 



BIOGRAPHY 

Vinayagamoorthy Balachandran was born on October 15, 1952, in 
Jaffna, Sri Lanka. He entered the University of Sri Lanka, Peradeniya, 
as the second best student in the nation and earned B.Sc. (Eng.) Honors 
degree in civil engineering in March, 1975. He was awarded Quickshaws 
Scholarship— 1973 and E.O.E. Pereira Scholarship — 1974 for the best 
performance made in second and third year examinations. Upon graduation 
he worked as an assistant lecturer in the same university. 

He was awarded a scholarship by the Asian Institute of Technology, 
Bangkok, Thailand, to continue graduate studies and obtained a Master of 
Engineering degree in structural engineering and mechanics in April 
1977. Then he worked as a consulting engineer at T. H. Chuah and 
Associates, Singapore, until July, 1977. Later he joined the University 
of Sri Lanka, Peradeniya, as assistant lecturer in civil engineering and 
worked until August 1978. 

He was admitted to the University of Florida, Gainesville, in the 
fall of 1978 on a graduate assistantship and was awarded the Ph.D degree 
in civil engineering in the fall of 1984. 

He is an associate member of American Society of Civil Engineers 
and Institution of Civil Engineers— London, and member of Tau Beta Pi — 
Engineering Honor Society. 



418 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 



0, 



Dr. Clifford 0. Hays7~Jr, 
Professor of Civil Engineering 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 



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/ 



Dr. MOrris W. Self 

Professor of Civil Engineering 



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I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 



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A 



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Dri. John M. Lybas v 
Assistant Professor ofLXivil 
Engineering 



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I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 



£/7/ e JCl+YlM^* 



Dr. U. H. Kurzweg 

Professor of Engineering Sciences 



I certify that I have read this study and that in my opinion it 
conforms to acceptable standards of scholarly presentation and is fully 
adequate, in scope and quality, as a dissertation for the degree of 
Doctor of Philosophy. 




Dr. Z. R. Pop-'Stojahovic 
Professor of Mathematics 



This dissertation was submitted to the Graduate Faculty of the 
College of Engineering and to the Graduate School, and was accepted as 
partial fulfillment of the requirements for the degree of Doctor of 
Philosophy. 



December 1984 



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Aaj~U> 



Dean, College of Engineering 



Dean for Graduate Studies and 
Research